User:Chojullius

Logarithmic Decrement

The logarithmic decrement may be used to estimate the damping ratio of a second order system from an oscillatory response. The logarithmic decrement is defined as the natural log of the ratio of the size of two peaks, n periods apart:$$\delta_n = ln(\frac{P_i}{P_{i+n}})$$. This ratio may be used to estimate the damping ratio with following equation:$$\varsigma = \frac{\delta_n}{((n+2{\pi})^2+{(\delta_n)^2})^{1/2}}$$