For the unity feedback shown in Fig. P 3. 5, where

\[G(s)=\frac{K}{s(s+3)(s+4)(s+5)}\]

Obtain the following:

(a) display a root locus and pause

(b) draw a close-up of the root locus where the axes go from -2 to 0 on the real axis and -2 to 2 on the imaginary axis

(c) overlay the $15 %$ overshoot line on the close-up root locus(d) allow you to select interactively the point where the root locus crosses the $15 %$ overshoot line, and respond with the gain at that point as well as all of the closedloop poles at that gain

(e) find the step response at the gain for $15 %$ overshoot.

Fig. P 3. 5

R(s) + G(s) C(s)