What are $LC$ oscillations?

$A$ $2 \mu F$ capacitor is charged to $50 V$ by a battery. The battery is removed after the capacitor is fully charged. At time $t=0$,a $10 mH$ coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is (in $A s^{-1}$)

Compare $LC$ oscillations and forced damped oscillations in mechanics.

An $LC$ circuit contains a $20 \, mH$ inductor and a $50 \, \mu F$ capacitor with an initial charge of $10 \, mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t = 0$. At what time is the energy stored completely magnetic? $t = \dots \, ms$

Initially,the key was placed on $(1)$ until the capacitor got fully charged. Now,the key is placed on $(2)$ at $t = 0$. Find the minimum time when the energy in both the capacitor and the inductor will be the same.

In an oscillating $LC$ circuit,the maximum charge on the capacitor is $Q$. What is the charge on the capacitor when the energy is stored equally between the electric and magnetic fields?