Forced Oscillations with Nonlinear Restoring Force

Abstract

Forced oscillations with nonlinear restoring force are studied in transient states as well as in steady states. The differential equations which govern the oscillations are under some. restrictions transformed to the form : dy/dx = Y(x, y)/X(x, y), and the integral curves of this equation are studied according to Poincare and Bendixson with the basic idea that the singularities of the above equation are correlated with the periodic steady states of oscillation and the integral curves with transient states. With this method of investigation we have first studied the harmonic oscillations in Part I, then the subharmonic oscillations in Part II. In both cases the theoretical analyses are compared with experimental results, and the satisfactory agreement is found between them.