Question

Find the steady-state oscillation of y+cy+y=r(t)y^{\prime \prime}+c y^{\prime}+y=r(t) with c>0c>0 and r(t) as given. (Show the details of your work.)

r(t)=sin3tr(t)=\sin 3 t

Solution

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We find the steady-state solution for the ODE

y+cy+y=r(t)=sin3t,  π<t<π,  c>0.y''+cy'+ y=r(t)=\sin 3t,\;-\pi<t<\pi,\;c>0.

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