$12\mathrm{.}12$ A certain unity$-$feedback system has the following open$-$loop system transfer function.

$G(s)=\frac{K}{s^3+6s^2+5s}$

Obtain the Bode plots and compute the phase and gain margins for

a$.K=10$

b$.K=100$

c$.$ Determine the upper limit on $K$ for the system to be stable. Which is the limiting factor: the phase margin or the gain margin?

Use sisotool to do your analysis. copy and past the sisotool window and then discuss your results in words.