SMC A System Is Described by The Following Differential Equation Problems

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unafz12

Mathematics

Santa Monica College

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1. (30 points) A system is described by the following differential equation: dy dy + 8 dt2 +12y(t) = 2 dt dt dr +5r(t) dy y(0) = 0, = 1; dt (a) Compute the zero-input response. (b) Compute the impulse response, h(t). (c) Determine the zero-state response when the input is r(t) = 4u(t). Feel free to use Table 2.1 (attached at the end of this exam). (d) Determine the total response of the system. Table 2.1: Convolution Table Open table as spreadsheet No. x1(1) 1 x(t) |x2(1) 811-T) u(t) x1(t)* x2(t) = x2(t)*xu(t) x(t-T) 2 Mult) 1 pir - 3 u(t) 4 Mtu(t) u(t) e^2u(t) tu(1) lei plat (1) λι - λα λι 4 λ. torruft) etu(t) 6 tentu(t) 7 Nu(t) entu(t) Mtu(t) şr educa) errult) IN NIIN 22+1(N-k)! 1N4T (1) ko 8 Mult) | Mult) M+N+ (1) tem fu(t) 12'u(t) MINI (M + N + :)! F431 - +(21-22)redil - (1) (-22) MINI M+N+leu(1) (N + M + :)! 10 Menu(t) Menu(t)
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