Logarithmic decrement

Logarithmic decrement, δ {displaystyle delta } , is used to find the damping ratio of an underdamped system in the time domain. Logarithmic decrement, δ {displaystyle delta } , is used to find the damping ratio of an underdamped system in the time domain. 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. The logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks: where x(t) is the overshoot (amplitude - final value) at time t and x(t + nT) is the overshoot of the peak n periods away, where n is any integer number of successive, positive peaks.