$(1)$ Given the system

a$)$ Use root locus to design a proportional controller so that the closed$-$loop system has a $.$ Calculate the closed loop $w_n.$ Plot root locus by hand.

b$)$ Design a PI controller so that the closed$-$loop $=0\mathrm{.}7$ ad the response time is similar to pur't $($a$).$ plot the root locusiby hand.

c$)$ Plot the closed$-$loop step responses for parts a$)$ and b$).$

Repeat problem $(1)$ above with.

$G(s)=\frac{35}{(s+1)(s+3)(s+10)}$

Use matlab's ritool to plot the root locus.