$2.$ In the figure, the capacitor is initially charged when $\backslash ($ S$\_\{1\}\backslash )$ is open and $\backslash ($ S$\_\{2\}\backslash )$ is closed. Then $\backslash (\backslash$mathrm$\{$S$\}\_\{1\}\backslash )$ is thrown closed at the same instant that $\backslash (\backslash$mathrm$\{$S$\}\_\{2\}\backslash )$ is opened so that the capacitor is shorted across the inductor. $(14$ points$)$

$($a$)$ Find the frequency of oscillation.

$(4)$

$($b$)$ Find the maximum values of change on the capacitor and the current in the circuit. $(6)$

$($c$)$ Write the charge on the capacitor and the current in the circuit as a function of time. $(4)$