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Example: Force Driving a Mass

Consider a force $ f(t)$ driving a mass $ m$ to produce a velocity $ v(t)=\dot{x}(t)$ at the driving point. By Newton's 2nd law,

$\displaystyle f(t) \;=\;m\, \dot{v}(t) \;\longleftrightarrow\;F(s) = ms\,V(s)
$

if $ v(0)=0$ , so that

$\displaystyle \zbox{R_m(s) \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;\frac{F(s)}{V(s)} \;=\;ms}
$




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``Lumped Elements, One-Ports, and Passive Impedances'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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