$2.($a$)$ Consider the circuit in Figure $2\mathrm{.}1$ where the switch $\backslash ($ S $\backslash )$ has been at position a for a very long time. The switch is moved to position bat $\backslash ($ t$=0\backslash ).$ Determine the voltage $\backslash ($ v$($t$)\backslash )$ for $\backslash ($ t$>0\backslash )$ using time domain analysis.

Figure $2\mathrm{.}1$