Symmetry and pauses in some singular forced oscillations

Abstract

The response of some oscillatory circuit to a periodic singular input wave, possessing “pauses” that are not directly seen via the frequency spectrum of the oscillations, but very simply result from the reflection symmetry of the input waveform and that of the forced describing equation, is considered. The symmetry argument is similar for linear and nonlinear (quasi-linear) versions of the oscillatory circuit or equation, and the simplicity of the argument is a noticeable methodological point. The pauses are not ideal; the inevitable power losses in the circuit cause breaking of the reflection symmetry of the response function, and some relatively weak oscillations occur in the pauses. The pause oscillations can be resonantly suppressed with respect to the non-pause oscillations. The discussion is oriented towards scientists and teachers.