Consider a second-order system (Y(s) / U(s)=omega_{n}^{2} /left(s^{2}+2 zeta omega_{n} s+omega_{n}^{2} ight)), which has two poles at

Consider a second-order system \(Y(s) / U(s)=\omega_{n}^{2} /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}\right)\), which has two poles at \(-4 \pm 4 \mathrm{j}\).

a. Determine the undamped natural frequency \(\omega_{n}\) damping ratio \(\zeta\), and damped natural frequency \(\omega_{\mathrm{d}}\) of the system.

b. Estimate the rise time \(t_{\mathrm{r}^{\prime}}\) overshoot \(M_{\mathrm{p}}\) peak time \(t_{\mathrm{p}}\) and \(2 \%\) settling time \(t_{\mathrm{s}}\) in the unit-step response for the system.