Analysis of Damped Mass-Spring Systems for Sound Synthesis
Don Morgan, Sanzheng Qiao · EURASIP Journal on Audio Speech and Music Processing · 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 massspring 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: mass-spring system, sound synthesis, stability, accuracy, symplectic Euler. 1