A tape recorder has a speed control system with unity negative feedback $.$

It$$s transfer function, G$($s$)$ is given as:

$($a$)$ Draw the poles and zeroes of the root locus for K$,$ and use the angle and

magnitude conditions to confirm that the dominant roots are s $=0\mathrm{.}35$ j

$0\mathrm{.}80$ when K $=6\mathrm{.}5$

$($b$)$ For the dominant roots of part $($a$),$ calculate the $5\%$ settling time and

overshoot for a step input