STEADY$-$STATE DAMPED OSCILLATIONS

Find the steady$-$state oscillations of $y^{\text{'}\text{'}}+c{y}^{\text{'}}+y=r(t)$

with $c>0$ and $r(t)$ as given. Note that the spring constant

is $k=1.$ Show the details. In Probs. $14-16$ sketch $r(t).$

$r(t)={\displaystyle \underset{n=1}{\overset{N}{}}}(a_{n}cosnt+b_{n}sinnt)$

$r(t+2)=r(t)r(t)=t({}^2-t^2)r(t+2)=r(t)r(t)=tif-\frac{}{2}-$ and

$r(t+2)=r(t)$

$r(t)=$

$tif-\frac{}{2}$

onlly problem $16$