Revisiting the Coulomb-Damped Harmonic Oscillator

TL;DR

This paper introduces a sinusoidal resistive force model to approximate Coulomb friction in harmonic oscillators, providing an analytically solvable alternative that better captures dry friction effects compared to traditional viscous damping models.

Contribution

It proposes a novel sinusoidal approximation for Coulomb friction in oscillators, enabling closed-form solutions and improved modeling of dry friction effects.

Findings

The sinusoidal model closely fits numerical Coulomb damping results.

Analytic solutions are derived and validated against numerical simulations.

The approach enhances understanding of dry friction in oscillatory systems.

Abstract

The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is the model's only free parameter. We seek the value of this parameter that yields the best fit and obtain a closed-form analytic solution, which is shown to nicely fit the numerical one.