On the stability of the state of equilibrium of an oscillator with infinitely great frequency of proper oscillations

Abstract

A problem of the stability of the state of equilibrium of an oscillator with infinitely great frequency of proper oscillations under periodic in time perturbations, is considered. It is shown that in general case the problem can be solved by consideration of the linear approximation of the perturbation only. In singular case a procedure of the construction of a constant whose sign defines the character of the stability or instability, is presented. Namely, if this constant is negative then the state of equilibrium is asymptotically stable; in the opposite case it is unstable.