5. (20% total) For a second order system with transfer function $T(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$, subjected to a unit step input, the desired dynamic response is specified in the following:
3% ? $M_p$ ? 10%
$t_s$ ? 1.1 sec
$t_r$ ? 0.1 sec
where $M_p$ is the overshoot, $t_s$ is the settling time when the system oscillates within ±1% of the steady-state value, and $t_r$ is the rise time of 90% of the steady-state value, as defined in the lecture notes.
Show in the s-plane, in Figure 4, the region within which the requirements of the dynamic response are met.