Chapter 5.P1, Problem 3P

Suppose that the impressed voltage is prescribed by the square wave

$e(t)=\{\begin{array}{cc}1,& 0\le t\le \pi /\sqrt{2}\\ -1,& \pi /\sqrt{2}\le t\le \sqrt{2}\pi \end{array}$

And $e(t)$ has period $\sqrt{2}\pi$.

Assuming zero initial condition as stated in Problem $1$, find an expression for $q(t)$ and plot the graphs of $e(t)$ and $q(t)$ on the same set of coordinate axes. Explain the behaviour of $q(t)$. Assuming the at time $t=0$ the charge on the capacitor is zero and the currents $i_1$ and $i_1$.