The switch in the Figure below is connected to point a for a long time. After the switch is thrown to point $b,$ determine

a$.$ the frequency of oscillations in the $LC$ circuit.

b$.$ the maximum charge that appears on the capacitor,

c$.$ the maximum current in the inductor,

d$.$ the total energy the circuit possesses at $t=3\mathrm{.}00s.$

e$.$ At $t=0\mathrm{.}6ms,$ find the charge on the capacitor and the current in the circuit.