Find the transfer function h(@) = ŷ(@)/x(@) of the following ODE and plot its magnitude. y"(t) + y'(t)+ y(t) = x(1) HINT: Take the Fourier Transform of the ODE to obtain -a²y(@) +iaỹ(0) + y(@) = x(0) Giving h(w) = M(w) 1 ²+ io +1 x() The magnitude of the transfer function is then |h(o)= 1 √(₁-w²} + a² h(@) 05 0.5 07 0.5 04 03 0.2 0.6 0.8 1 12 e 1.6 1.8 2

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