Question

For each of the following systems and inputs: Exercise 3.1 1. Check whether the system is stable. 2. If the system is stable, use frequency response to determine the steady state response? 3. For a stable system, the time to reach steady state can be estimated as four times the time constant of the slowest pole. When a system is stable, all poles are in the left half plane (LHP). The slowest pole is the one with the largest (least negative) real part. For each stable system, approximately how long will it take for the steady state condition to be achieved. The time constant is the reciprocal of the absolute value of the real part of the pole location. Problem System Input u(t) = sin(1t) u(t) = 10 sin(10t) u(t) = cos(5t) u(t) = sin(3t) u(t) = sin(wt) u(t) = cos(t) u(t) = sin(wt) u(t) = 10 sin(wt) u(t) = cos(3t) u(t) = sin(10t) u(t) = sin(wt) u(t) = sin(t) s2+101 1| H(s) = G+2s+1) H(s) = F10 2 3 H(s) = t5 4 H(s) = 10 5| Н() — — 6 H(s) = +10)(s+1) s-1 7 H(s) = 1010 8 H(s) = s+10 9 H(s) %3D s+3 +100 (s2+200s+100) H(s) H(s) = H(s) = 10 11 S-10 s-1 (s+10)(s+1) +4 (s+10)(s+1) 12 13 | Н() u(t) = cos(2t) %3D

need parts 1, 2, 11, 13