For the circuit of Figure P5.21, assume that switch $S_2$ is always open, and that switch $S_1$ has been closed for a long time and opens at $t=0$. At $t=t_1=3 \tau$, switch $S_1$ closes again.
a. Find the capacitor voltage, $v_c(t)$, at $t=0^{+}$.
b. Find an expression for $a_c(t)$ for $t>0$ and sketch the function.