Consider a unity feedback control system with the transfer function G(s) in the forward path. For each of the following transfer functions, sketch the root locus as K varies from 0 to and find the following: (i) Parts of the real axis that have root locus; (ii) Number of asymptotes, their angles, and their intersection with the real axis; (iii) Break-in and breakaway points (if any); (iv) The range of K for stability; (v) Points of intersection with the imaginary axis (if any); (vi) The value of K to yield a stable system with a pair of complex poles having a damping ratio of 0.5 (if possible). (a) G(s) (b) G(s) = K(S-2)(s-3) (s+1) (s+3) K(s+3) (S-1)(s+2)(s+5)