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State-Space Model of a Force-Driven Mass

Figure 1.6: Ideal mass $ m$ on frictionless surface driven by force $ f(t)$ .
\includegraphics{eps/forcemassintrosimp}

For the simple example of a mass $ m$ driven by external force $ f$ along the $ x$ axis, we have the system of Fig.1.6. We should choose the state variable to be velocity $ v={\dot x}$ so that Newton's $ f=ma$ yields

$\displaystyle \dot{v} \eqsp \frac{1}{m} f.
$

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


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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