(mathbb{A}) Consider a second-order system (Y(s) / U(s)=omega_{n}^{2} /left(s^{2}+2 zeta omega_{n} s+omega_{n}^{2} ight)). a. Write a MATLAB...

\(\mathbb{A}\) Consider a second-order system \(Y(s) / U(s)=\omega_{n}^{2} /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}\right)\).

a. Write a MATLAB m-file to plot the magnitude of the system's frequency response function for the following cases: \(\omega_{\mathrm{n}}=2 \mathrm{rad} / \mathrm{s}\) and \(\zeta=0.01,0.1,0.5\), and 1 . Summarize the effects of the damping ratio on the frequency-domain performance.

b. Repeat Part (a) for the following cases: \(\zeta=0.1\) and \(\omega_{n}=1,2\), and \(6 \mathrm{rad} / \mathrm{s}\). Summarize the effects of the natural frequency on the frequency-domain performance.