Logarithmic Decrement Calculator

✖The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.ⓘ Frequency Constant for Calculation [a]			+10% -10%
✖Time Period is the time taken by a complete cycle of the wave to pass a point.ⓘ Time Period [t_p]			+10% -10%

✖Logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks.ⓘ Logarithmic Decrement [δ]

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Formula

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Logarithmic Decrement

Formula

`"δ" = "a"*"t"_{"p"}`

Example

`"0.6"="0.2Hz"*"3s"`

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Logarithmic Decrement Solution

STEP 0: Pre-Calculation Summary

Formula Used

Logarithmic Decrement = Frequency Constant for Calculation*Time Period
δ = a*t_p
This formula uses 3 Variables

Variables Used

Logarithmic Decrement - Logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks.
Frequency Constant for Calculation - (Measured in Hertz) - The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.

STEP 1: Convert Input(s) to Base Unit

Frequency Constant for Calculation: 0.2 Hertz --> 0.2 Hertz No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = a*t_p --> 0.2*3

Evaluating ... ...

δ = 0.6

STEP 3: Convert Result to Output's Unit

0.6 --> No Conversion Required

FINAL ANSWER

0.6 <-- Logarithmic Decrement

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Frequency of Free Damped Vibrations » Logarithmic Decrement

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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< 9 Frequency of Free Damped Vibrations Calculators

Logarithmic Decrement using Natural Frequency

Go Logarithmic Decrement = (Frequency Constant for Calculation*2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))

Logarithmic Decrement using Circular Damping Coefficient

Go Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2))

Condition for Critical Damping

Go Critical Damping Coefficient = 2*Mass Suspended from Spring*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Logarithmic Decrement using Circular Damped Frequency

Go Logarithmic Decrement = Frequency Constant for Calculation*(2*pi)/Circular Damped Frequency

Damping Factor given Natural Frequency

Go Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)

Critical Damping Coefficient

Go Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency

Amplitude Reduction Factor

Go Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period)

Logarithmic Decrement

Go Logarithmic Decrement = Frequency Constant for Calculation*Time Period

Damping Factor

Go Damping Ratio = Damping Coefficient/Critical Damping Coefficient

Logarithmic Decrement Formula

Logarithmic Decrement = Frequency Constant for Calculation*Time Period
δ = a*t_p

What is damped free vibration?

Damped vibration occurs when the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped. The vibrations gradually reduce or change in frequency or intensity or cease and the system rests in its equilibrium position.

How to Calculate Logarithmic Decrement?

Logarithmic Decrement calculator uses Logarithmic Decrement = Frequency Constant for Calculation*Time Period to calculate the Logarithmic Decrement, The Logarithmic decrement formula is defined as the natural log of the ratio of the amplitudes of any two successive peaks. Logarithmic Decrement is denoted by δ symbol.

How to calculate Logarithmic Decrement using this online calculator? To use this online calculator for Logarithmic Decrement, enter Frequency Constant for Calculation (a) & Time Period (t_p) and hit the calculate button. Here is how the Logarithmic Decrement calculation can be explained with given input values -> 0.06 = 0.2*3.

FAQ

What is Logarithmic Decrement?

The Logarithmic decrement formula is defined as the natural log of the ratio of the amplitudes of any two successive peaks and is represented as δ = a*t_p or Logarithmic Decrement = Frequency Constant for Calculation*Time Period. The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass & Time Period is the time taken by a complete cycle of the wave to pass a point.

How to calculate Logarithmic Decrement?

The Logarithmic decrement formula is defined as the natural log of the ratio of the amplitudes of any two successive peaks is calculated using Logarithmic Decrement = Frequency Constant for Calculation*Time Period. To calculate Logarithmic Decrement, you need Frequency Constant for Calculation (a) & Time Period (t_p). With our tool, you need to enter the respective value for Frequency Constant for Calculation & Time Period and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Logarithmic Decrement?

In this formula, Logarithmic Decrement uses Frequency Constant for Calculation & Time Period. We can use 3 other way(s) to calculate the same, which is/are as follows -

Logarithmic Decrement = Frequency Constant for Calculation*(2*pi)/Circular Damped Frequency
Logarithmic Decrement = (Frequency Constant for Calculation*2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))
Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2))

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