(a) Use MATLAB to obtain the root locus plot of 2s 3 + 12s 2 + 16s + K = 0 for K ≥ 0. (b) Obtain the value of K required to give a dominant root pair having ζ = XXXXXXXXXXc) For this value of K,...

(a) Use MATLAB to obtain the root locus plot of 2s³
+ 12s²
+ 16s + K = 0 for K ≥ 0. (b) Obtain the value of K required to give a dominant root pair having ζ = 0.707. (c) For this value of K, obtain the unit-step response and the maximum overshoot, and evaluate the effects of the secondary root. The closed-loop transfer function is K/(2s³
+ 12s²
+ 16s + K).