Normal Mode Expansion of Damped Coupled Oscillators in 3 dimensions

TL;DR

This paper extends normal mode analysis to multi-dimensional damped and undamped coupled oscillators, providing a method to decouple and solve their equations of motion.

Contribution

It introduces a technique to analyze free and driven oscillations of coupled oscillators in multiple dimensions, including damping effects.

Findings

Decoupling of multi-dimensional oscillators simplifies analysis.

Normal mode expansion is applicable beyond one dimension.

Damped driven systems in higher dimensions are studied with velocity-dependent damping.

Abstract

In this paper, I aim to study free oscillations of a system of oscillators in more than one dimensions in the absence of damping. The basic approach lies in decoupling the motion in the individual perpendicular directions. Once the equations are decoupled, the existent techniques of Normal mode expansion for 1-dimensional oscillators are used to solve for the equations of motion. I also study the motion of a driven system of oscillators in higher dimensions in the presence of a velocity dependent damping force.