13. A system is described the following input/output differential equation, with zero initial conditions. \frac{d^2y(t)}{dt^2} + 2\frac{dy(t)}{dt} + y(t) = \frac{dx(t)}{dt} + x(t - 4) a) Determine the transfer function H(s) b) Determine the impulse response h(t)
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Taking the Laplace transform of each term, we have: s^2Y(s) - sy(0) - y'(0) + sY(s) - y(0) + Y(s)e^(-4s) = sX(s) - x(0) Since the initial conditions are zero, we can simplify the equation to: s^2Y(s) + sY(s) + Y(s)e^(-4s) = sX(s) Now, we can rearrange the Show more…
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