Next  |  Prev  |  Up  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Sinusoidal Driving Force

Let's drive a mass $ m$ sinusoidally at radian frequency $ \omega$ :

$\displaystyle f(t)=\cos(\omega t) = \frac{1}{2}e^{j\omega t}+\frac{1}{2}e^{-j\omega t}
$

The resulting velocity (using $ V(j\omega) = F(j\omega)/R_m(j\omega)$ ) is

\begin{eqnarray*}
v(t) &=& \frac{1}{jm\omega}\cdot\frac{1}{2}e^{j\omega t}+\frac{1}{jm(-\omega)}\cdot\frac{1}{2}e^{-j\omega t}\\
&=& \frac{1}{m\omega}\cdot\frac{1}{2j}e^{j\omega t}-\frac{1}{m\omega}\cdot\frac{1}{2j}e^{-j\omega t} \;=\;\frac{1}{m\omega}\sin(\omega t)
\end{eqnarray*}


Next  |  Prev  |  Up  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Download OnePorts.pdf
Download OnePorts_2up.pdf
Download OnePorts_4up.pdf
Visit the online book containing this material.

``Lumped Elements, One-Ports, and Passive Impedances'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-04-09 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]