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Damping Ratio

Damping ratio $ \zeta\isdeftext 1/(2Q)$ is defined to conveniently divide the underdamped, critically damped, and overdamped conditions at unity for a second-order system.

The damping ratio $ \zeta$ (zeta) is defined by

$\displaystyle \zeta \isdefs \frac{1}{2Q} \eqsp \frac{\alpha}{\omega_0}
$

where $ Q$ is defined above in Eq.(E.8) as the peak frequency divided by the peak bandwidth, and $ \alpha$ and $ \omega_0$ are defined above in Eq.(E.7).

As shown in Eq.(E.9), a damping factor of 1 is critically damped, while a damping factor less than 1 is underdamped, and $ \zeta>1$ is overdamped.


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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