Oscillations arising in a circuit under the influence of internal forces, such as a capacitor discharging through a resistance and inductance, or of a constant external force, such as a direct voltage. Both these conditions are analogous to a mechanical vibrating system being displaced from the neutral point.
The oscillations decay gradually, depending on the amount of damping in the circuit, with a frequency, f, termed the natural frequency; this is approximately equal to (LC)–2, where L is the inductance and C is the capacitance, when the resistance R in the circuit is small (see diagram). The amplitude of the current is given by
where the angular frequency ω is equal to 2πf, and A is a constant determined by the initial conditions. The maxima of successive oscillations lie on the curve
and the amplitudes (im, im+1) of successive maxima of the same sign decrease by a constant ratio. It can be shown that
where Q, the Q factor of the circuit, is given by
Compare forced oscillations.