Question

(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for the input X(t) = 24 cos(6t) u(t) by using Laplace Transform. + 6yle) = d– 2016) y(t) =

Answer 1

at goren dy + by H) = dr ) - 06) (1) gliên y0) = 1 giren Zenynput response do z)=0 dy + 6. d4 (t) =0 SYQJ-4003 +641)=0 sus-1 +683050 440 (546)= ka)- 576 les é let) dt 12) Zero Stoete gespense 720) co Now geven 24)= ē tufts SYW) + 6 449 ESX($) - X(5) ${}) } { 12 ( 346) = x 3 (<-) YETE S-L (5+1)(546)

VS28= 4 +-715 Inverse Lot Yzzl} tutt7e tot) . (3) YH = Zerostate Resperse + Zero is p grojpeste ya) = effects .euc - .86telt All

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