A system is described by the following second-order linear differential equation dt + 5 + 6y(t) = drey + (t) dut) + 2t d

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A System Is Described By The Following Second Order Linear Differential Equation Dt 5 6y T Drey T Dut 2t D 1 (43.24 KiB) Viewed 20 times

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A system is described by the following second-order linear differential equation dt + 5 + 6y(t) = drey + (t) dut) + 2t dt where y(0-) = 2, y' (0-) = 1, and the input + (t) = e-4u (t) 1. By taking the Laplace Transform of both sides of the equation above, express Y(s) the Laplace Transform of y(t) in terms of X(s) the Laplace Transform of x(t) and the initial conditions y (0-) and y' (0-). (10 points) Y(s) 2. Find the transfer function H (s) = . The transfer function is defined when X(8) there are no initial conditions. (10 points) 3. Solve the differential equation by finding the inverse Laplace Transform of Y(s) found in part 1 of this question. (10 points).