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<h2 class="hd hd-2 unit-title">12.1. Activity: Reconstructing the pole diagram from the Bode plot.</h2>
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<p>
Here you will use the Bode and Nyquist Plot Mathlet, position poles and zeros as needed to reproduce the two Bode gain plots as closely as you can – first for the system without the secondary, then for the system with both masses. </p>
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System with no secondary mass
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<p>
Including the voice coil, the system without the secondary mass is third order. The transfer function has the form </p>
<table id="a0000001196" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
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<td class="equation" style="width:80%; border:none">[mathjax]H(s) = \frac{1}{as^3 + bs^2 + cs + d}.[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none">&#160;</td>
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<p>
This function exhibits three poles. They may be real or complex &#8211; you have to decide. </p>
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The numerator in the transfer function is constant. How many zeros does the transfer function have? </p>
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<p>Using the Bode and Nyquist Plot Mathlet, position poles and zeros as needed to reproduce the Bode gain plot as closely as you can. Here is the Bode plot we found for the system without the secondary mass.</p>
<center><img src="/assets/courseware/v1/1b80b2cb7f9d492fa769520775256bb1/asset-v1:OCW+18.031+2019_Spring+type@asset+block/images_Bode2ndOrder.png" width="400" /></center>
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The mascot
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The denominator of the model of the mascot has degree five. How many poles does this indicate that the transfer function has? </p>
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The numerator has degree 2. How many zeros does the transfer function have? </p>
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Based on the Bode plot video, are the zeros likely to form a complex conjugate pair, or a pair of real zeros? </p>
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<p>Using the Bode and Nyquist Plot Mathlet, position poles and zeros as needed to reproduce the Bode gain plot of the mascot as closely as you can.</p>
<center><img src="/assets/courseware/v1/334dac854cf161d8ebaa1d8b3e461ef5/asset-v1:OCW+18.031+2019_Spring+type@asset+block/images_TunedMassDamper_Plots-2b.png" width="600" /><br />Measured frequency: response of the Mascot system</center>
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Share your answers on the forum. Discuss what choices you encountered in developing your pole diagram. </p>
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