Chapter 7.6, Problem 20E

The current $I\left(t\right)$ in an LC series circuit is governed by the initial value problem

$I^{″}\left(t\right)+4I\left(t\right)=g\left(t\right);$

$I\left(0\right)=1$, $I^{\prime }\left(0\right)=3,$

where

$g\left(t\right)=\{\begin{array}{l}3\sin t,0\le t\le 2\text{π,}\\ 0,2\text{π}<t.\end{array}$

Determine the current as a function of time $t$.