$A$ charged $10 \mu F$ capacitor is connected to a $16 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit?

$A$ 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?

For which two reasons is the discussion of $LC$ oscillations not realistic?

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycle/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

$A$ $LC$ circuit is in the state of resonance. If $C = 0.1 \mu F$ and $L = 0.25 \ H$. Neglecting the ohmic resistance of the circuit,what is the frequency of oscillations in $Hz$?

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?