Sketch the root locus with respect to K for the equation 1 + KG1H1(3) = 0 and the following choices of G1H1(s). Be sure to give the asymptotes, arrival, and departure angles at any complex zero or pole, and the frequency of any imaginary-axis crossing GH1(s) = GH(s) = (s + s (s + 2) (s + 4s + 68) 10) (s + 4s + 85) [(s + 1) + 1] s (s + 2) (s + 3) Sketch the root locus for the system shown below and find the following a. The range of gain to yield stability. b. The value of gain that will yield a damping ratio of 0.707 for the system dominant poles c. The value of gain will yield closed-loop poles that are critically damped. R(s) + K s(s+3)(s + 7)(s+8) (s +30) (s +20s +200) C(s)