# Dynamical analysis of mass-spring models using Lie algebraic methods

## TL;DR

This paper applies Lie algebraic methods to analyze the dynamics of mass-spring vibrational systems, providing solutions for various configurations including finite arrays, bridging classical and quantum-inspired techniques.

## Contribution

It introduces Lie algebraic techniques to solve complex vibrational systems, extending classical methods with quantum-inspired mathematical tools.

## Key findings

- Solutions for finite circular and linear arrays using classical methods.
- Application of Lie algebraic methods to more complex arrays.
- Unified framework connecting classical and quantum approaches.

## Abstract

The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in quantum optical systems. We further study some more complicated arrays where the solutions are given by using Lie algebras.