Chapter 7.6, Problem 19E

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

$I^{″}\left(t\right)+2I^{\prime }\left(t\right)+2I\left(t\right)=g\left(t\right);$

$I\left(0\right)=10,I^{\prime }\left(0\right)=0,$

where

$g\left(t\right):=\{\begin{array}{l}20,0<t<3\text{π,}\\ 0,3\pi <t<4\pi ,\\ 20,\text{4π}<t.\end{array}$

Determine the current as a function of time $t$. Sketch $I\left(t\right)$ for $0<t<8\text{π}$.