Find the transfer function h() = y()/x() of the following ODE and plot its magnitude. y(t)...

 

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Find the transfer function h() = y()/x() of the following ODE and plot its magnitude. y"(t) + y(t) + y(t) = x(t) HINT: Take the Fourier Transform of the ODE to obtain -w²y(@) +iay(@) + y(@) = x(0) Giving y(@) 1 ²+ io +1 x(0) The magnitude of the transfer function is then h(w) = |ĥ(w) = 1 √(1-0²) + @² h(@)| 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 020 0.2 0.4 0.6 0.8 (10) 1 12 1.4 1.6 1.8 2 Find the transfer function h() = y()/x() of the following ODE and plot its magnitude. y"(t) + y(t) + y(t) = x(t) HINT: Take the Fourier Transform of the ODE to obtain -w²y(@) +iay(@) + y(@) = x(0) Giving y(@) 1 ²+ io +1 x(0) The magnitude of the transfer function is then h(w) = |ĥ(w) = 1 √(1-0²) + @² h(@)| 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 020 0.2 0.4 0.6 0.8 (10) 1 12 1.4 1.6 1.8 2

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