State-Space Model of a Force-Driven Mass

For the simple example of a mass driven by external force along the axis, we have the system of Fig.1.6. We should choose the state variable to be velocity so that Newton's yields

This is a first-order system (no vector needed). We'll look at a simple vector example below in §1.3.7.

---

Previous: Forming Outputs
Next: Numerical Integration of General State-Space Models

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.