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 for the reaction force of an ideal mass , with Robert Hooke's spring force law (published in 1676), where 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 [259, 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 [406].

---

Previous: History of Modal Expansion
Next: Sampling Theory

Order a Hardcopy of Physical Audio Signal Processing

---

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.