Consider the following closed$-$loop system:whereG$($s$)=$ s $+1$s$($s $+5)($s$2+4$s $+8).$You want to analyze how the control K affects closed$-$loop stability using a root$-$locus.Problem $1.(10$ points$)$ Check if so $=2$ is a loci or not using the angle condition.Problem $2.(10$ points$)$ Find the aymptotes angles and a real merging point.Problem $3.(10$ points$)$ Find the departure angles at the open$-$loop poles and the arrival angle atthe open$-$loop zero.Problem $4$ & $5.(10$ points each$)$ Repeat Problem $2$ and $3$ withG$($s$)=1$s$($s$2+4$s $+5).$