1. A second-order system has the following transfer function that describes its response: F(s) = 9 s² + as + 9 A. For α = 3, calculate the following performance specifications of the system: • Natural frequency (n) • Damping ratio (C) . Estimated rise time and settling time with ±5% change (tr, ts) Estimated overshoot (MP) B. Label (a) ±5% range of steady state, (b) tr, (c) ts, and (d) Mp on the step response curve below. (You may also use a larger copy of this graph attached in the next page) 1.4 Response Amplitude 1.2 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(Sec) C. For α = 9, calculate the following performance specifications of the system: Natural frequency (On) • Damping ratio (C) Estimated overshoot (MP) D. Is the system in part C overdamped, underdamped or critically damped? Explain why. Plot the expected response curve of this system in the same plot you used to answer part B.