An oscillator circuit consists of an inductance of $0.5 \ mH$ and a capacitor of $20 \ \mu F$. The resonant frequency of the circuit is nearly......$Hz$

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?

$A$ 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?

An $LCR$ circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having a damping constant $b$,the correct equivalence would be:

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

Show that in the free oscillations of an $LC$ circuit,the sum of energies stored in the capacitor and the inductor is constant in time.