What is the use of logarithmic decrement

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

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 {and}} n = 1,2, ... \ ,,} \)

\ ({\ displaystyle x_ {i}} \) = Amplitude of the deflection at the measuring point \ ({\ displaystyle i} \). \ ({\ displaystyle x_ {i + n}} \) = amplitude of the deflection at the measuring point \ ({\ displaystyle i + n} \). \ ({\ displaystyle \ delta} \) = decay constant. D = degree of damping. \ ({\ displaystyle \ omega _ {0}} \) = natural angular frequency of the undamped oscillation. T = period of oscillation.

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










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Status of information: 11/23/2020 12:05:08 PM CET

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