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Open Access

Analysis of Damped Mass-Spring Systems for Sound Synthesis

EURASIP Journal on Audio, Speech, and Music Processing20092009:947823

Received: 26 July 2008

Accepted: 20 February 2009

Published: 8 June 2009


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.


Differential EquationDecay RateAcousticsFull ArticleEuler Method

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Authors’ Affiliations

Department of Computing and Software, McMaster University, Hamilton, Canada


© D. Morgan and S. Qiao. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.