$($Automatic Controls Homework Help Please$)$

$2)[50$ pts total$]$ Consider the unity feedback control system shown in Fig. $2,$ below, where $K$ is a tunable gain. The questions below pertain to the root locus of the closed$-$loop poles as the gain is varied from $K=0$ to $K.$

a$)[15$ points$]$ What are the real axis segments of the root locus?

b$)[15$ points$]$ How many asymptote does the root locus have, and what are their angles?

c$)[15$ points$]$ Is the point $s=-2+j$ in the root locus? If yes, what value of $K$ places a closed$-$loop pole at that location?

d$)[5$ points$]$ Do a rough sketch the root locus by hand.

Figure $2$: Unity feedback control system.