Consider a second-order system (Y(s) / U(s)=omega_{n}^{2} /left(s^{2}+2 zeta omega_{n} s+omega_{n}^{2} ight)). Sketch the allowable region of

Consider a second-order system \(Y(s) / U(s)=\omega_{n}^{2} /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}\right)\). Sketch the allowable region of the poles in the s-plane if the requirements for the system's unit-step response are \(M_{\mathrm{p}} \leq 25 \%, 5 \%\) settling time \(t_{\mathrm{s}} \leq 2 \mathrm{~s}\), and rise time \(t_{\mathrm{r}} \leq 0.5 \mathrm{~s}\).