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Mass-Spring Resonators

Since a harmonic oscillator is produced by a simple mass-spring system, a mechanical generator for the harmonic basis functions of Bernoulli is readily obtained by equating Newton's second law $ f=m\ddot{x}$ for the reaction force of an ideal mass $ m$ , with Robert Hooke's spring force law $ f=-kx$ (published in 1676), where $ k$ is an empirical spring constant [65]. Hooke (1635-1703) was a contemporary of Newton's who carried out extensive experiments with springs in search of a spring-regulated clock [261, pp. 274-288]. Hooke's law was generalized to 3D by Cauchy (1789-1857) as the familiar linear relationship between six components of stress and strain.A.7

Elementary mass-spring models have found much use in computational physical models for purposes of sound synthesis [69,92]. For example, a mass-spring oscillator is typically used to model a brass-player's lips [4], piano hammers [44], and is sometimes included in woodwind-reed models [409].

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University