$3.(20$ points$)$ Consider the circuit below. Assume the switch has been in its initial position for a long time, and it switches position as indicated at $\backslash ($ t$=0\backslash ).$

b$.$ Sketch $\backslash (\backslash$boldsymbol$\{$v$\}(\backslash$boldsymbol$\{$t$\})\backslash )$ as voltage vs$.$ time.

c$.$ How much energy is stored in the capacitor at $\backslash (\backslash$boldsymbol$\{$t$\}=\backslash$mathbf$\{0\}\backslash )?($Answer: $3\mathrm{.}2$ mJ $)$