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].
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History of Modal Expansion
