Consider the feedback system of Figure 11.3(b) with (a) Sketch the root locus...

Consider the feedback system of Figure 11.3(b) with

(a) Sketch the root locus for K > 0 and K < 0 when a =1/2.

(b) Repeat part (a) when a = -1/2.

(c) With a = —1/2, find a value of K for which the closed-loop impulse response is of the form

for some values of the constants A, B, and a, with | α | < 1. (Hint: What must the denominator of the closed-loop system function look like in this case?)