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: <math> Q = \frac{1}{2\zeta}, </math>
: <math> Q = \frac{1}{2} \sqrt{1 + \left(\frac{n2\pi}{\ln \frac{x(t)}{x(t+nT)}}\right)^2}. </math>
The damping ratio can then be used to find the natural frequency ''ω''<sub>''n''</sub> of vibration of the system from the damped natural frequency ''ω''<sub>''d''</sub>'':''
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