Comparative analysis of linear and non-linear free vibrations of harmonic oscillator

Abstract

Free vibrations of a harmonic oscillator in the form of a mathematical pendulum in linear and nonlinear formulations are considered. Their comparative analysis is carried out as a conservative system with one degree of freedom. To solve a nonlinear differential equation, the finite difference method and Euler' s scheme are used. Specific examples are given, the limits of the mathematical pendulum deviations angles, at which the solutions of linear and nonlinear problems practically coincide, are determined. The law of potential and kinetic energy sum conservation is used for the oscillations of conservative systems. The conclusions are drawn for the practical application of the results obtained.