Damping Ratio - Q Factor and Decay Rate

Q Factor and Decay Rate

The factors Q, damping ratio ζ, and exponential decay rate α are related such that


\zeta = \frac{1}{2 Q} = { \alpha \over \omega_0 }.

When a second-order system has (that is, when the system is underdamped), it has two complex conjugate poles that each have a real part of ; that is, the decay rate parameter represents the rate of exponential decay of the oscillations. A lower damping ratio implies a lower decay rate, and so very underdamped systems oscillate for long times. For example, a high quality tuning fork, which has a very low damping ratio, has an oscillation that lasts a long time, decaying very slowly after being struck by a hammer.

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