Abstract
The nonlinear-oscillator equation is examined with an approximate technique worked out for the linear-oscillator equation. This approximate technique is valid for β/ω<1, where β is the damping term and ω 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.
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