Question

US) Long answer problems 15 points per problem (30 total) — Expected to take 10-12 minutes per problem 9. For the second order system, G(s) = 2x2 +88+16 answer the following questions: (a) Is the system undamped, underdamped, critically damped, or overdamped? Calcu- late ( and w.. (b) Find the system response, *(t), for the step input, ur(t). Show your partial fraction expansion work. Identify the steady state and transient portions of the response.

Answer 1

Giveno A snof forced damped oscillation Analysis G()=K) UR) N8²+ bstR 28? +8846 comparina No2, bre, RE 2=16 6 8 E = $ drem 0-707 252x16 Conce Eli (system is under damped) 1612 2.42 rad Is. 6 Response of eftem a quen by 16 8 - Eront x6: con coscwat do 2 a= tani for the tea 35-33º X(t) = 0.0625 alatt [ 1.4146 cos 62.010 - 35-39) m Steady lott : 0.0625 Cos (2.017 ~ 35:30) Pransient state :0.625 (-1.4148 light cos (2:01t-38530)

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