Logarithmic decrement

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The logarithmic decrement , formula symbol (large lambda) is a measure of the damping behavior in freely oscillating vibration systems. ${\displaystyle \Lambda }$

The logarithmic decrement is calculated from the natural logarithm of the ratio of the amplitude of any two deflections in the same direction.

${\displaystyle \Lambda =\ln {\frac {x_{i}}{x_{i+1}}}={\frac {1}{n}}\ln {\frac {x_{i}}{x_{i+n}}}={\frac {2\pi \delta }{\sqrt {\omega _{0}^{2}-\delta ^{2}}}}\ =\delta \cdot T,}$

With

${\displaystyle \delta =\omega _{0}D{\text{ und }}n=1,2,...\,,}$

${\displaystyle x_{i}}$= Amplitude of the deflection at the measuring point . = Amplitude of the deflection at the measuring point . = Decay constant . D = degree of damping . = Natural angular frequency of the undamped oscillation. T = period of oscillation. ${\displaystyle i}$ ${\displaystyle x_{i+n}}$ ${\displaystyle i+n}$ ${\displaystyle \delta }$ ${\displaystyle \omega _{0}}$

The determination of is quite easy by practical measurement of the amplitude . The degree of damping can then easily be determined from this. ${\displaystyle \Lambda }$