Problem $3(12$ points$)$: Consider the system shown below. Let I$=$c$=4.$ The performance specifications require

that $\backslash$tau $=0\mathrm{.}2$ seconds.

Compute the required gain values for each of the following cases. You can assume the disturbance T$\_($d$)$ is negligible

for these cases:

a$\mathrm{.}1$:$\backslash$zeta $=0\mathrm{.}707$

b$\mathrm{.}2$:$\backslash$zeta $=1$

c$.$a pole separation factor of $10($the two real roots are a factor of $10$ apart$)$ with the time

constant being approximately $0\mathrm{.}2$ seconds.