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Force Driving a Mass

Suppose now that we wish to drive the mass along a frictionless surface using a variable force $ f(n)$ . This is similar to the previous example, except that we now want the traveling-wave components of the force on the mass to sum to $ f(n)$ instead of 0 :

$\displaystyle f(n) = f^{{+}}(n) + f^{{-}}(n)

Since $ f(n)$ and $ f^{{-}}(n)$ are given, $ f^{{+}}(n)$ must be computed as $ f^{{+}}(n) = f(n) - f^{{-}}(n)$ . This is shown in Fig.F.11.

Figure F.11: Wave digital mass driven by external force $ f(n)$ .

The simplified form in Fig.F.11b can be interpreted as a wave digital spring with applied force $ f(n)$ delivered from an infinite source impedance. That is, when the applied force goes to zero, the termination remains rigid at the current displacement.

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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