## Alternating Current

# LC Oscillations

When a charged capacitor C having an initial charge q_{0} is discharged through an inductor L, the charge and current in the circuit starts oscillating simple harmonically. If the resistance of the circuit is zero, no energy is dissipated as heat. The total energy associated with the circuit is constant.

Frequency of oscillation is given by

\omega = \frac{1}{\sqrt{LC}}

### View the Topic in this video From 24:43 To 57:40

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1. Oscillates with a natural frequency \omega_{0} = \frac{1}{\sqrt{LC}}

2. A mass *m* oscillating with frequency ω_{0}, the equation is \frac{d^{2}x}{dt^{2}} + \omega_{0}^{2}x = 0