Consider the system shown in Figure P3.12, where (a=25 mathrm{~cm}), (ell_{1}=50 mathrm{~cm}), and (ell_{2}=30 mathrm{~cm}). Here, (k=1,100

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Consider the system shown in Figure P3.12, where \(a=25 \mathrm{~cm}\), \(\ell_{1}=50 \mathrm{~cm}\), and \(\ell_{2}=30 \mathrm{~cm}\). Here, \(k=1,100 \mathrm{~N} / \mathrm{m}, m=2 \mathrm{~kg}\), and the damping ratio is 0.1 .

Figure P3.12 

image text in transcribed

a. Derive the transfer function \(\frac{x(s)}{y(s)}\).

b. Find poles and zeros of the transfer function.

c. Construct Bode plots for the frequency response function.

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