logarithmic decrement

The damping ratio is then found from the logarithmic decrement:

This is called the logarithmic decrement.

The paper described the theory of oscillating circuits having sources of both linear and logarithmic decrements within themselves.

Logarithmic decrement, δ, is used to find the damping ratio of an underdamped system in the time domain.

Logarithmic decrement (a method for determining damping ratio)

A quantitative measure of the damping is provided by the logarithmic decrement defined as the logarithmic decrease in amplitude per cycle.

The logarithmic decrement is the natural log of the ratio of the amplitudes of any two successive peaks:

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.

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.

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.