Logarithmic Decrement

\_▐ló-gә-^▐rith-mik ^▐de-krә-mәnt\ (Δ) In a damped, vibrating system, the natural logarithm of the ratio of the amplitude of any oscillation to the amplitude of the succeeding oscillation. Where damping is mild, the ratio of the amplitude of any oscillation to the amplitude of the succeeding oscillation. Where damping is mild, the ratio of amplitudes several vibrations apart will usually give a more accurate estimate. The equations are:

$$ \Delta {\rm\ = ln(}A_i /A_{i{\rm + 1}} {\rm )\ and }\ \Delta {\rm\ =(l/n) {\cdot} ln(}A_i /A_{i{\rm + n}} {\rm )}$$