What is an $LC$ circuit?

Solve the differential equation of $L-C$ circuit and obtain the expression of current.

In an $LC$ circuit,the capacitor has a maximum charge $q_0$. The value of $\left| \frac{di}{dt} \right|_{\max }$ is

$A$ capacitor of capacity '$C$' is charged to a potential difference of '$V_1$'. The plates of the capacitor are then connected to an ideal inductor of inductance '$L$'. The current through the inductor when the potential difference across the capacitor reduces to '$V_2$' is:

Explain how $LC$ oscillations take place in the circuit.

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 $t=0$.
$(a)$ What is the total energy stored initially? Is it conserved during $LC$ oscillations?
$(b)$ What is the natural frequency of the circuit?
$(c)$ At what time is the energy stored $(i)$ completely electrical (i.e.,stored in the capacitor)? $(ii)$ completely magnetic (i.e.,stored in the inductor)?
$(d)$ At what times is the total energy shared equally between the inductor and the capacitor?
$(e)$ If a resistor is inserted in the circuit,how much energy is eventually dissipated as heat?