Consider the second-order system shown in Fig. 1.92. The system is subjected to unit step input. Derive the expression for the output variable. Determine the time domain specifications \(T, t_{s}, t_{d}, M_{p}\), and \(t_{p}\). What is the resonant peak \(M_{r}\) and resonant frequency \(\omega_{r}\) in the frequency domain?

Figure 1.92

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R(s) + G(s) = 13 s(s+4) C(s)