Harmonic oscillators at resonance, perturbed by a non-linear friction force

TL;DR

This paper extends previous work on resonant harmonic oscillators by introducing a more general analysis of nonlinear friction forces, highlighting differences in boundary value problems.

Contribution

It provides a broader theoretical framework for analyzing nonlinear friction effects at resonance, improving upon prior results with a modified argument.

Findings

Generalized results for nonlinear friction at resonance

Differences identified between oscillatory and boundary value problems

Enhanced understanding of periodic solutions in nonlinear systems

Abstract

This note is an addendum to the results of P.O. Frederickson and A.C. Lazer [1], and A.C. Lazer [4] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [4] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem.