Question $5$

A unity feedback system has a loop transfer function:

$G_{c}G(s)=\frac{Ks}{s^3+5s^2+10}$

$($a$)$ Sketch the root locus.

$[15$ marks$]$

$($b$)$ Determine the gain $K$ when the complex roots of the characteristic equation have a $$ approximately equal to $0\mathrm{.}66.$

$[10$ marks$]$