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Physical Audio Signal Processing
Elementary Physics, Mechanics, and Acoustics
Work = Force times Distance = Energy
Energy Conservation in the
Mass-Spring System
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Energy Conservation in the Mass-Spring System
Recall that Newton's second law applied to a mass-spring system, as in §B.1.4, yields
gives
![\begin{eqnarray*}
0
&=& m{\ddot x}(t){\dot x}(t) + k\,x(t){\dot x}(t)\\
&=& m\...
...{d}{dt} \left[ E_m(t) + E_k(t) \right]\\
&=& \frac{d}{dt} E(t).
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img2682.png)
Thus, Newton's second law and Hooke's law imply conservation of energy in the mass-spring system of Fig.B.2.
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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.
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