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  • Research Article
  • Open Access

Analysis of Damped Mass-Spring Systems for Sound Synthesis

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

https://doi.org/10.1155/2009/947823

  • Received: 26 July 2008
  • Accepted: 20 February 2009
  • Published:

Abstract

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.

Keywords

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

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Computing and Software, McMaster University, Hamilton, ON, L8S 4L7, Canada

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