Modeling of free and forced oscillations of the inertial nonstationary harmonic oscillator

摘要

Analytic and computer models of a harmonic oscillator with slowly varying natural frequency of oscillations are considered. The representation of Green's function in the form of harmonic oscillation with an envelope and a phase depending on the natural frequency is used. The excitation function is used to describe forced oscillations induced by an external harmonic influence. The case of a harmonic oscillator with linearly varying natural frequency of oscillations is considered. Analytic expressions for free and forced oscillations are obtained; the relationship between natural frequency scanning parameters and excitation function parameters is established. The results of numerical simulation of charged particle oscillations in a quadruple radio frequency electric field with a linearly varying amplitude with a uniform excitation field superimposed on it confirm correctness of the analytical calculations obtained.