# Bode Plots and Harmonic Response

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a) Draw the Bode plot (on semi-logarithmic graph paper) of the transfer function.

see attached

aii) From the Bode plot, what would the approximate harmonic response of the above system to an input, u(t)=sin(2t)? Confirm your answer by simple calculation.

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##### Solution Summary

Bode plots are calculated, and the resulting Bode plots (magnitude and phase plots) are added as an attachment. Additionally, the approximate harmonic response is calculated from the Bode plot by getting the magnitude and phase from the magnitude and phase plots, respectively.

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P(s) = 3( s/2 + 1) e^(-0.05s)/[(s/5)^2+2*0.5*(s/5)+1]

= 37.5*(s+2)/(s^2+5s+25)* e^(-0.05s)

ai) The Bode plot of P(S) is shown in the attached file.

The magnitude plot is exactly correct, but in the phase plot please include the effect of the time delay due to the e^(-0.05s) term by adding the term

-0.05w for each value of ...

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