The frequency of oscillation of the current in the given circuit is:

What is meant by $LC$ circuit? What are $LC$ oscillations?

$LC$-oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

In the $LCR$ circuit shown in the figure,the ac driving voltage is $V = V_m \sin \omega t$.
$(a)$ Write down the equation of motion for $q(t)$.
$(b)$ At $t = t_0$,the voltage source is removed and $R$ is short-circuited. Write down the energy stored in each of $L$ and $C$ at this instant.
$(c)$ Describe the subsequent motion of charges.

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

$A$ capacitor of capacitance $C$ has an initial charge $Q_0$ and is connected to an inductor $L$ as shown. At $t = 0$,the switch $S$ is closed. What is the current through the inductor when the energy in the capacitor is three times the energy of the inductor?