Consider the $($open$-$loop$)$ system $P(s)$ given as:

$P(s)=\frac{10}{s(s+3{)}^2}$

i$)$ Compute the phase and gain crossover frequencies for this system, and then use these to compute the gain and phase margins.

ii$)$ SKETCH the Nyquist and Bode plots for this system, labelling all of the points calculated in part i$)$ above on both plots.

iii$)$ Suppose I use a simple proportional controller $K($with unity negative feedback$).$ Compute the value of $K$ that achieves a compensated system with a phase margin of $70.$