A unity feedback system has

$G(s)=\frac{K}{(s+2)(s+4)(s+6)}$

$($a$)$ Sketch the root locus for the control system for $=0\mathrm{.}80,$

$[14$ marks$]$

$(b)$ Determine the gain $K$ when the complex roots have a damping ratio $of=0\mathrm{.}8.$

$[6$ marks$]$