(a) Investigate the validity of a second-order step response approximation for the transfer function below: 185.71(s + 7) G(S) = (s +6.5)(s + 10) (s + 20) (b) Derive the transfer function of a second order system that yields a 12.3% overshoot and a settling time of 2.0 second. Then, categorize the type of natural response and identify the characteristic of the poles. (c) Figure Q2(C) shows a step response of a rotational mechanical system. Based on your understanding on engineering control field, analyze the step response and determine the percentage overshoot and the settling time. Then, suggest the transfer function of the system. 25 20 15 Response 10 5 0 0 1 4 5 2 3 Time (seconds) Figure Q2(c)