On Bêthenod's Phenomenon

Abstract

It is well known that if one places a pendulum with an iron bob in the neighborhood of a coil fed from the main, one observes that the pendulum attains its stationary oscillation. It seems that there is no necessity of a rational ratio between the frequency of the pendulum which is close to its proper one and the frequency of the main which is very high compared with that of the pendulum.
In this paper, this phenomenon, first treated by J. Bêthenod, is studied analytically and it is concluded that the dissipated energy of the pendulum is supplied from the main by some retarded action of the electromagnetic force of the coil.
The method of analysis can be applied to a class of electromechanical phenomena in which the mechanical system is maintained in oscillation at a frequency of or near its proper one at the expense of the energy supplied from the electrical system. Further, an electromechanical rotator based on the same principle as the Bêthenod's pendulum was devised and the experiment of which seems to support the validity of the analysis.
Finally, the case in which the electrical system is a series ferroresonant circuit is discussed and it is pointed out that the energy of the pendulum is supplied by the oscillation hysteresis of the nonlinear circuit. As an application of this phenomenon, an electric master clock without electric contact was devised.