3. Consider the system with closed-loop transfer function H(s)= s2 4 4 +2s+4(s+i+i)(s+1—A a. Using contour integration evaluate the time response of the system given the input is equal to x(t) = tr(t). Denote the contour used in your answer. b. Given the response
,, [ sin(,E1t)) y(t) = 1 — e’ cos0130+ — Determine the the natural frequency (o„, the damped natural frequency ay, and the damping factor C.