$2)[10$pts$]$ Consider a unity feedback system with $()=()().$ a$)$ Show that the system cannot operate with a settling time of $$ secs and a percent overshoot of $1\mathrm{.}5\%$ with a simple gain adjustment. b$)$ Design a lead compensator so that system meets the transient response characteristics of part $($a$).$ Specify the compensator$$s pole, zero, and the required gain.