The physical model: modeling and simulating the instrumental universe
Representations of musical signals
The computer music tutorial
Elementary Differential Equations With Mathematica
Elementary Differential Equations With Mathematica
Physically based sound modelling
Organised Sound
An Introduction to Computer Simulation Methods: Applications to Physical Systems (3rd Edition)
An Introduction to Computer Simulation Methods: Applications to Physical Systems (3rd Edition)
Analysis of damped mass-spring systems for sound synthesis
EURASIP Journal on Audio, Speech, and Music Processing
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This paper examines the stability and accuracy of mass-spring systems used in sound synthesis. We show that the standard method used in mass-spring systems has no numerical damping, but does have frequency warping and is unstable at frequencies above 1/π times the sampling rate. We compare the standard method with two higher order numerical methods: the fourth order Runge-Kutta, and the VEFRL algorithm, a fourth order symplectic algorithm. We find that the VEFRL algorithm is much more accurate than the standard method, but that this increase in accuracy does not noticeably affect the quality of the sound produced by the mass-spring system when used to simulate a vibrating string. The increased accuracy of the VEFRL method may, however, be useful for mass-spring spring systems used in physics or engineering requiring high accuracy.