# Damping ratio (ζ)

A value that determines how quickly the oscillations of a vibrating system decay — the oscillations decay more quickly for larger $$\zeta$$. For light damping (typical of ultrasonic systems, at least unloaded) the following relations are valid (see Thompson (1) equations 2.3-4, p. 44 and 3.10-5, p. 74, respectively) —

\begin{align} \label{eq:14701a} \zeta = \frac{\delta}{2 \, \pi} \end{align}

where —

 $$\delta$$ = log decrement

\begin{align} \label{eq:14702a} \zeta = \frac{1}{2 \, Q} \end{align}

where —

 $$Q$$ = quality factor

Also see —
Attenuation
Bandwidth
Loss tangent