Extracting Physical Quantities

Since we are using a force-wave simulation, the state variable (delay element output) is in units of physical force (newtons). Specifically, . (The physical force is, of course, 0, while its traveling-wave components are not 0 unless the mass is at rest.) Using the fundamental relations relating traveling force and velocity waves

where here, it is easy to convert the state variable to other physical units, as we now demonstrate.

The velocity of the mass, for example, is given by

Thus, the state variable can be scaled by to ``read out'' the mass velocity.

The kinetic energy of the mass is given by

I.e., the square of the state variable can be scaled by to produce the physical kinetic energy associated with the mass.

---

Previous: ``Piano hammer in flight''
Next: Force Driving a Mass

Order a Hardcopy of Physical Audio Signal Processing

---

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.