The physical model: modeling and simulating the instrumental universe
Representations of musical signals
The electrical engineering handbook
The electrical engineering handbook
A digital signal processing primer, with applications to digital audio and computer music
A digital signal processing primer, with applications to digital audio and computer music
Vibration Simulation Using MATLAB and ANSYS
Vibration Simulation Using MATLAB and ANSYS
Elementary Differential Equations With Mathematica
Elementary Differential Equations With Mathematica
Physically based sound modelling
Organised Sound
TAO: a physical modelling system and related issues
Organised Sound
Accuracy and stability in mass-spring systems for sound synthesis
Proceedings of the 2008 C3S2E conference
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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 ofmass-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.