Solved: CAS EXPERIMENT. Maximum Output Term. Graph and

Chapter 11, Problem 11.1.108

(choose chapter or problem)

Find a general solution of the ODE \(y^{\prime \prime}+\omega^{2} y=r(t)\) with r(t) as given. (Show the details of your work.)

\(r(t)=\left\{\begin{array}{rlr}t+\pi  \text { if }  -\pi<t<0 \\ -t+\pi  \text { if }  0<t<\pi\end{array}\right.\)

and \(r(t+2 \pi)=r(t),|\omega| \neq 0,1,3, \cdots\)

Text Transcription:

y” + omega^2 y = r(t)

r(t) = {t + pi  if  - pi < t < 0 \\ -t + pi  if   0 < t < pi

r(t + 2 pi) = r(t), |omega| neq 0,1,3, cdots