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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(5) 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 - a²ŷ(0) + iaỹ(a) + y(@) = x(w) Giving h(o)= = y(@) 1 x(@) - @²+ io +1 The magnitude of the transfer function is then |ħ(w) = 1 1- @²} + @² |h(@) 0.5 0.8 0.7 0.6 0.5 0.4 0.3 e 0.2 0,4 0.6 0.8 (10) e 1 1.2 1.4 1.6 1.8 2
Transcribed Image Text:(5) 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 - a²ŷ(0) + iaỹ(a) + y(@) = x(w) Giving h(o)= = y(@) 1 x(@) - @²+ io +1 The magnitude of the transfer function is then |ħ(w) = 1 1- @²} + @² |h(@) 0.5 0.8 0.7 0.6 0.5 0.4 0.3 e 0.2 0,4 0.6 0.8 (10) e 1 1.2 1.4 1.6 1.8 2
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