<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@vertical+block@ps4-checkvertical" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <h2 class="hd hd-2 unit-title">Pset 4 checker</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+ES.1803+2023_Fall+type@html+block@0487ba15f6954f7f960c80ec265e5e51"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@html+block@0487ba15f6954f7f960c80ec265e5e51" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p><a href="/assets/courseware/v1/bfcec4108bbee8525ce3ee3f84a97f45/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/mites_1803_s24_ps4.pdf" target="[object Object]">Problem set 4 (PDF)</a></p> <p></p> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-1-i-check" class="problems-wrapper" role="group" aria-labelledby="ps4-1-i-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-1-i-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 1-i &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-i-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; To check your answers put them in the appropriate box and click the &amp;#8216;Check&#39; button. The checker can do arithmetic. So, 3^2, [mathjaxinline]5/3[/mathjaxinline] and [mathjaxinline]3*4[/mathjaxinline] are okay. &lt;/p&gt; &lt;p&gt; Unless otherwise stated the checker expects numerical answers to 3 significant digits. &lt;/p&gt; &lt;p&gt; For formulas you should use Matlab notation. Remember to use a * for multiplication, i.e. [mathjaxinline]3*x[/mathjaxinline] &lt;b class=&#34;bf&#34;&gt;NOT &lt;/b&gt; [mathjaxinline]3x[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; The checker knows many of the standard functions. Use exp(x) and ln(x) for the exponential and natural log functions. &lt;/p&gt; &lt;p&gt; The formula checker expects a specific letter for the variables, so be sure to use the one specified. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 1, System (i).&lt;/b&gt; For these problems, use the variable w, the parameters m, b, k and the functions [mathjaxinline]P()[/mathjaxinline] and [mathjaxinline]Arg()[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; For the formal answers, you should use the functions P and Arg. For the detailed answers, use [mathjaxinline]m[/mathjaxinline], [mathjaxinline]b[/mathjaxinline], [mathjaxinline]k[/mathjaxinline] &lt;/p&gt; &lt;p&gt; Remember to write [mathjaxinline]i\omega[/mathjaxinline] as i[mathjaxinline]*[/mathjaxinline]w. For the magnitude of a complex number use &lt;b class=&#34;bf&#34;&gt;abs()&lt;/b&gt;. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (i): Formal [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-i-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-i-check_2_1&#34; id=&#34;input_ps4-1-i-check_2_1&#34; aria-describedby=&#34;status_ps4-1-i-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-i-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-i-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-i-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-i-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-i-check_2_1_dynamath&#34; name=&#34;input_ps4-1-i-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (i): Detailed [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-i-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-i-check_3_1&#34; id=&#34;input_ps4-1-i-check_3_1&#34; aria-describedby=&#34;status_ps4-1-i-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-i-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-i-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-i-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-i-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-i-check_3_1_dynamath&#34; name=&#34;input_ps4-1-i-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (i): Formal [mathjaxinline]\phi (\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-i-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-i-check_4_1&#34; id=&#34;input_ps4-1-i-check_4_1&#34; aria-describedby=&#34;status_ps4-1-i-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-i-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-i-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-i-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-i-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-i-check_4_1_dynamath&#34; name=&#34;input_ps4-1-i-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 1-i&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-1-i-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-1-i-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-i-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-i-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-i-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-1-ii-check" class="problems-wrapper" role="group" aria-labelledby="ps4-1-ii-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-1-ii-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 1-ii &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-ii-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 1, System (ii).&lt;/b&gt; Same instructions as for System (i). &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (ii): Formal [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-ii-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-ii-check_2_1&#34; id=&#34;input_ps4-1-ii-check_2_1&#34; aria-describedby=&#34;status_ps4-1-ii-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-ii-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-ii-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-ii-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-ii-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-ii-check_2_1_dynamath&#34; name=&#34;input_ps4-1-ii-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (ii): Detailed [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-ii-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-ii-check_3_1&#34; id=&#34;input_ps4-1-ii-check_3_1&#34; aria-describedby=&#34;status_ps4-1-ii-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-ii-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-ii-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-ii-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-ii-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-ii-check_3_1_dynamath&#34; name=&#34;input_ps4-1-ii-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (ii): Formal [mathjaxinline]\phi (\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-ii-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-ii-check_4_1&#34; id=&#34;input_ps4-1-ii-check_4_1&#34; aria-describedby=&#34;status_ps4-1-ii-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-ii-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-ii-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-ii-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-ii-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-ii-check_4_1_dynamath&#34; name=&#34;input_ps4-1-ii-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 1-ii&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-1-ii-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-1-ii-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-ii-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-ii-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-ii-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-1-iii-check" class="problems-wrapper" role="group" aria-labelledby="ps4-1-iii-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-1-iii-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 1-iii &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-iii-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 1, System (iii).&lt;/b&gt; Same instructions as for Systems (i) and (ii). &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (iii): Formal [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-iii-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-iii-check_2_1&#34; id=&#34;input_ps4-1-iii-check_2_1&#34; aria-describedby=&#34;status_ps4-1-iii-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-iii-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-iii-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-iii-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-iii-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-iii-check_2_1_dynamath&#34; name=&#34;input_ps4-1-iii-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (iii): Detailed [mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-iii-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-iii-check_3_1&#34; id=&#34;input_ps4-1-iii-check_3_1&#34; aria-describedby=&#34;status_ps4-1-iii-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-iii-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-iii-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-iii-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-iii-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-iii-check_3_1_dynamath&#34; name=&#34;input_ps4-1-iii-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (iii): Formal [mathjaxinline]\phi (\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-iii-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-iii-check_4_1&#34; id=&#34;input_ps4-1-iii-check_4_1&#34; aria-describedby=&#34;status_ps4-1-iii-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-iii-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-iii-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-iii-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-iii-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-iii-check_4_1_dynamath&#34; name=&#34;input_ps4-1-iii-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 1-iii&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-1-iii-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-1-iii-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-iii-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-iii-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-iii-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-1-x-check" class="problems-wrapper" role="group" aria-labelledby="ps4-1-x-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-1-x-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 1-x &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-1-x-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 1, output row [mathjaxinline]x(t)[/mathjaxinline].&lt;/b&gt; Give the output row in the table. The problem asks for the &amp;#8216;formal solution&#39; written in terms of [mathjaxinline]g(\omega )[/mathjaxinline] and [mathjaxinline]\phi (\omega )[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Use the variable t, &amp;#8201; parameters w, B &amp;#8201; and functions g(w) and phi(w) &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (i): [mathjaxinline]x(t)[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-x-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-x-check_2_1&#34; id=&#34;input_ps4-1-x-check_2_1&#34; aria-describedby=&#34;status_ps4-1-x-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-x-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-x-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-x-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-x-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-x-check_2_1_dynamath&#34; name=&#34;input_ps4-1-x-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (ii): [mathjaxinline]x(t)[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-x-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-x-check_3_1&#34; id=&#34;input_ps4-1-x-check_3_1&#34; aria-describedby=&#34;status_ps4-1-x-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-x-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-x-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-x-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-x-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-x-check_3_1_dynamath&#34; name=&#34;input_ps4-1-x-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (iii): [mathjaxinline]x(t)[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-1-x-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-1-x-check_4_1&#34; id=&#34;input_ps4-1-x-check_4_1&#34; aria-describedby=&#34;status_ps4-1-x-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-1-x-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-1-x-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-1-x-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-1-x-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-1-x-check_4_1_dynamath&#34; name=&#34;input_ps4-1-x-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 1-x&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-1-x-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-1-x-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-x-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-x-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-1-x-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-5" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-2-check" class="problems-wrapper" role="group" aria-labelledby="ps4-2-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-2-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 2 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-2-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 2.&lt;/b&gt; Give the practical resonance frequency for the three systems. &lt;/p&gt; &lt;p&gt; Use the parameters m, b, k. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Note.&lt;/b&gt; For some of these, there is only a resonance frequency for certain combinations of the parameters. The checker does not ask about these, but you need to indicate them on your paper. &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;2(a)&lt;/b&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (i): [mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-2-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-2-check_2_1&#34; id=&#34;input_ps4-2-check_2_1&#34; aria-describedby=&#34;status_ps4-2-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-2-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-2-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-2-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-2-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-2-check_2_1_dynamath&#34; name=&#34;input_ps4-2-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;2(b)&lt;/b&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (ii): [mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-2-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-2-check_3_1&#34; id=&#34;input_ps4-2-check_3_1&#34; aria-describedby=&#34;status_ps4-2-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-2-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-2-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-2-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-2-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-2-check_3_1_dynamath&#34; name=&#34;input_ps4-2-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;2(c)&lt;/b&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;System (iii): [mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-2-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-2-check_4_1&#34; id=&#34;input_ps4-2-check_4_1&#34; aria-describedby=&#34;status_ps4-2-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-2-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-2-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-2-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-2-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-2-check_4_1_dynamath&#34; name=&#34;input_ps4-2-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 2&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-2-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-2-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-2-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-2-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-2-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-6" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-3-check" class="problems-wrapper" role="group" aria-labelledby="ps4-3-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-3-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 3 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-3-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;Problem 3(a)&lt;/b&gt; Give the practical resonance frequencies the various setting of System (i). If there is none, give the answer &#39;none&#39; (without the quotes). &lt;/p&gt; &lt;p&gt; When doing this remember that once you&#39;ve clicked on the [mathjaxinline]\omega[/mathjaxinline] slider, you can move it with the arrow keys. You can also get a numerical value for the gain, by putting your mouse in the gain graph window. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;3(a).i.&lt;/b&gt; For [mathjaxinline]k=1[/mathjaxinline], [mathjaxinline]b=0.5[/mathjaxinline], give the resonant frequency in the applet to 2 decimal places or &#39;none&#39;: &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_2_1&#34; id=&#34;input_ps4-3-check_2_1&#34; aria-describedby=&#34;status_ps4-3-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_2_1_dynamath&#34; name=&#34;input_ps4-3-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;3(a).ii&lt;/b&gt; For [mathjaxinline]k=1[/mathjaxinline], [mathjaxinline]b=1.5[/mathjaxinline], give the resonant frequency in the applet to 2 decimal places or &#39;none&#39;: &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_3_1&#34; id=&#34;input_ps4-3-check_3_1&#34; aria-describedby=&#34;status_ps4-3-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_3_1_dynamath&#34; name=&#34;input_ps4-3-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;3(a).iii&lt;/b&gt; &lt;/p&gt; &lt;p&gt; For [mathjaxinline]k=1[/mathjaxinline], [mathjaxinline]b=0.5[/mathjaxinline], give the resonant frequency from your problem 2 formula to 3 decimal places or &#39;none&#39;: (Hint: in the applet [mathjaxinline]m=1[/mathjaxinline].) &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_4_1&#34; id=&#34;input_ps4-3-check_4_1&#34; aria-describedby=&#34;status_ps4-3-check_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_4_1_dynamath&#34; name=&#34;input_ps4-3-check_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; For [mathjaxinline]k=1[/mathjaxinline], [mathjaxinline]b=1.5[/mathjaxinline], give the resonant frequency from your problem 2 formula to 3 decimal places or &#39;none&#39;: &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_5_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_5_1&#34; id=&#34;input_ps4-3-check_5_1&#34; aria-describedby=&#34;status_ps4-3-check_5_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_5_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_5_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_5_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_5_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_5_1_dynamath&#34; name=&#34;input_ps4-3-check_5_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;3(a).iv&lt;/b&gt; &lt;/p&gt; &lt;p&gt; For [mathjaxinline]k=1[/mathjaxinline], give the value of [mathjaxinline]b[/mathjaxinline] where resonance disappears from the applet to 2 decimal places: &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]b[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 5&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_6_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_6_1&#34; id=&#34;input_ps4-3-check_6_1&#34; aria-describedby=&#34;status_ps4-3-check_6_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_6_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_6_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_6_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_6_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_6_1_dynamath&#34; name=&#34;input_ps4-3-check_6_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; For [mathjaxinline]k=1[/mathjaxinline], give the value of [mathjaxinline]b[/mathjaxinline] where resonance disappears from your problem 2 formula to 3 decimal places: &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]b[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 6&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-3-check_7_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-3-check_7_1&#34; id=&#34;input_ps4-3-check_7_1&#34; aria-describedby=&#34;status_ps4-3-check_7_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-3-check_7_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-3-check_7_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-3-check_7_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-3-check_7_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-3-check_7_1_dynamath&#34; name=&#34;input_ps4-3-check_7_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;3(b)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 3&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-3-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-3-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-3-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-3-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-3-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-7" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-4-check" class="problems-wrapper" role="group" aria-labelledby="ps4-4-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-4-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 4 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-4-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;4(a)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;4(b)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;4(c)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 4&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-4-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-4-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-4-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-4-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-4-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-8" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-5-check" class="problems-wrapper" role="group" aria-labelledby="ps4-5-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-5-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 5 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-5-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;5(a)&lt;/b&gt; Give the formula for the periodic solution. Use the symbols &lt;tt class=&#34;tt&#34;&gt;R, L, C, E_0, w, t&lt;/tt&gt; and &lt;tt class=&#34;tt&#34;&gt;phi(w)&lt;/tt&gt;. (Here [mathjaxinline]\phi (w)[/mathjaxinline] stands for the phase lag.) &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]V_ R(t)[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-5-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-5-check_2_1&#34; id=&#34;input_ps4-5-check_2_1&#34; aria-describedby=&#34;status_ps4-5-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-5-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-5-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-5-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-5-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-5-check_2_1_dynamath&#34; name=&#34;input_ps4-5-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; Give the formula for the phase lag. Use the symbols R, L, C, E0, w. You can use the function arctan2(x,y) (&lt;i class=&#34;it&#34;&gt;note the order of the arguments&lt;/i&gt;), This automatically knows the correct quadrant. On your paper you should use [mathjaxinline]\tan ^{-1}()[/mathjaxinline] and specify the possible quadrants. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\phi (\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-5-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-5-check_3_1&#34; id=&#34;input_ps4-5-check_3_1&#34; aria-describedby=&#34;status_ps4-5-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-5-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-5-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-5-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-5-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-5-check_3_1_dynamath&#34; name=&#34;input_ps4-5-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;5(b)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;5(c)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;5(d)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 5&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-5-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-5-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-5-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-5-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-5-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-9" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-6-check" class="problems-wrapper" role="group" aria-labelledby="ps4-6-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-6-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 6 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-6-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;6(a)&lt;/b&gt; Give the formula for the gain. Use the symbols w, m, b, k. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]g(\omega )[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-6-check_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-6-check_2_1&#34; id=&#34;input_ps4-6-check_2_1&#34; aria-describedby=&#34;status_ps4-6-check_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;70&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-6-check_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-6-check_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-6-check_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-6-check_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-6-check_2_1_dynamath&#34; name=&#34;input_ps4-6-check_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bf&#34;&gt;6(b)&lt;/b&gt; Give the formula for the resonant frequency. Use the symbols m, b, k, &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _ r[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_ps4-6-check_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;text-input-dynamath_data inline&#34; data-preprocessor=&#34;MJxPrep&#34;/&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+ES.1803+2023_Fall+type@asset+block/MJxPrep.js&#34;/&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_ps4-6-check_3_1&#34; id=&#34;input_ps4-6-check_3_1&#34; aria-describedby=&#34;status_ps4-6-check_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;70&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_ps4-6-check_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_ps4-6-check_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_ps4-6-check_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_ps4-6-check_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_ps4-6-check_3_1_dynamath&#34; name=&#34;input_ps4-6-check_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;6(c)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 6&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-6-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-6-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-6-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-6-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-6-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-10" data-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-course-id="course-v1:MITx+ES.1803+2023_Fall" data-graded="False" data-block-type="problem" data-has-score="True" data-usage-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="88506ad2383811f0ad1b0e09798aea1b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_ps4-7-check" class="problems-wrapper" role="group" aria-labelledby="ps4-7-check-problem-title" data-problem-id="block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check" data-url="/courses/course-v1:MITx+ES.1803+2023_Fall/xblock/block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;ps4-7-check-problem-title&#34; aria-describedby=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Problem 7 &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+ES.1803+2023_Fall+type@problem+block@ps4-7-check-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;7(a)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bf&#34;&gt;7(b)&lt;/b&gt; &lt;em&gt;No answer checker given.&lt;/em&gt; &lt;b class=&#34;bf&#34;&gt;Hint: the resonant frequency is plotted on the imaginary axis.&lt;/b&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Problem 7&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_ps4-7-check&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_ps4-7-check&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-7-check-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-7-check-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;ps4-7-check-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>