On Extraordinary Phenomena in a Non-linear Forced Oscillation

Abstract

The non-linear forced oscillation represented by \ddotx−dF(x)⁄dx=pcosωt is discussed. Transforming this equation to the variational form, the Ritz method is applied to obtain the solution in the form of Fourier series. Concerning this solution, extraordinary points of two different kinds are distinguished. This method is applied to find the jumping voltage of a circuit containing iron reactor, and result obtained is in good agreement with Katano’s experiment.