Force Driving a Mass

Suppose now that we wish to drive the mass along a frictionless surface using a variable force . 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 instead of 0:

Since and are given, must be computed as . This is shown in Fig.F.9.

The simplified form in Fig.F.9b can be interpreted as a wave digital spring with applied force 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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Subsections

• A More Formal Derivation of the Wave Digital Force-Driven Mass

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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.