Skip to main content

Analysis of Damped Mass-Spring Systems for Sound Synthesis


There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs, and dampers. Numerical methods are required to approximate the differential equation of a mass-spring system. The standard numerical method used in implementing mass-spring systems for use in sound synthesis is the symplectic Euler method. Implementers and users of mass-spring systems should be aware of the limitations of the numerical methods used; in particular we are interested in the stability and accuracy of the numerical methods used. We present an analysis of the symplectic Euler method that shows the conditions under which the method is stable and the accuracy of the decay rates and frequencies of the sounds produced.

Publisher note

To access the full article, please see PDF.

Author information



Corresponding author

Correspondence to Don Morgan.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Morgan, D., Qiao, S. Analysis of Damped Mass-Spring Systems for Sound Synthesis. J AUDIO SPEECH MUSIC PROC. 2009, 947823 (2009).

Download citation


  • Differential Equation
  • Decay Rate
  • Acoustics
  • Full Article
  • Euler Method