Please see attachment.
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 ...
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.