he open$-$loop transfer function $($loop gain$)$ of a unity negative feedback control system is

L$($s$)=$ K

s$($s $+4)$

The desired system response to a step input is specified as peak time Tp $2$sec and percent overshoot P O $5\%.$

a$)(8$ points$)$ Determine whether both specifications can be met simultaneously by selecting the right value of

K$.$ What is the range of K for which both specifications can be met simultaneously?

b$)(2$ points$)$ Find the values of K for the step response of the system to have oscillations