The logarithmic decrement is the natural log of the ratio of the amplitudes of any two successive peaks:
2.
"' Logarithmic decrement "', \ delta, is used to find the damping ratio of an underdamped system in the time domain.
3.
This relation is only meaningful for underdamped systems because the logarithmic decrement is defined as the natural log of the ratio of any two successive amplitudes, and only underdamped systems exhibit oscillation.
4.
The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
5.
Finally, in 1895 he furnished a complete theory of the phenomenon of electric resonance, involving a method of utilizing resonance experiments for the determination of the wavelengths, and especially of the damping ( the logarithmic decrement ) of the oscillations in the transmitter and the receiver of the electric oscillations.
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