Effect of sliding friction in harmonic oscillators

TL;DR

This paper introduces an analytical model that incorporates sliding and viscous friction into harmonic oscillator equations, validated through experiments with a quartz tuning fork and atomic force microscopy.

Contribution

It presents a novel analytical model that separates sliding and viscous damping effects in harmonic oscillators, supported by experimental validation.

Findings

Model accurately predicts damping contributions

Experimental data agrees with theoretical predictions

Sliding friction significantly affects oscillator behavior

Abstract

Sliding friction is ubiquitous in nature as are harmonic oscillators. However, when treating harmonic oscillators the effect of sliding friction is often neglected. Here, we propose a simple analytical model to include both viscous and sliding fiction in common harmonic oscillator equations, allowing to separate these different types of dissipation. To compare this model with experimental data, a nanometric vibration was imposed on a quartz tuning fork, while an atomic force microscope tip was used to disturb its motion. We analyzed tuning fork resonance curves and `ring down' experiments and for each case calculated the amount of sliding friction and of viscous damping, finding an agreement between the two different experiments and the model proposed.