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Mass Velocity

\begin{figure}\centering
\input fig/wdhammer.pstex_t
\\
\end{figure}

Force-wave simulations easily provide velocity outputs:

\begin{eqnarray*}
v(n) &=& v^{+}(n) + v^{-}(n) = \frac{f^{{+}}(n)}{m} - \frac{f^...
...(n)}{m} \\
&=& \frac{x(n)}{m} + \frac{x(n)}{m}= \frac{2}{m}x(n)
\end{eqnarray*}

Thus, the mass velocity is simply the state variable $ x(n)$ scaled by $ 2/m$.


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Download SMAC03S.pdf
Download SMAC03S_2up.pdf

``Recent Developments in Musical Sound Synthesis Based on a Physical Model'', by Julius O. Smith III, (Stockholm Musical Acoustics Conference (SMAC-03), August 6--9, 2003).
Copyright © 2006-02-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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