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Logarithmic decrement, \delta, is used to find the damping ratio of an underdamped system in the time domain.
For underdamped vibrations, the damping ratio is also related to the logarithmic decrement \delta via the relation
lnnatural logarithmsnatural log
The logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks:
Thus logarithmic decrement also permits evaluation of the Q factor of the system:
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