The effect of damping on some nonlinear oscillators

The nonlinear-oscillator equation is examined with an approximate technique worked out for the linear-oscillator equation. This approximate technique is valid for beta/omicron less than 1, where beta is the damping term and omicron the oscillation frequency. It is shown that damping in the nonlinear oscillator produces a second oscillation which is adequately described by the double periodicity of the elliptic function. If the damping term is permitted to vanish, the double periodicity again becomes a single periodicity. Since the nonlinear oscillator is described by a second-order differential equation with two independent solutions each with its own frequency, the nonlinear oscillator has two modes of decay, a low frequency mode and a high frequency mode relating to these solutions. It is suggested that this double mode of decay may relate to the two modes of decay of ball lightning.