Logarithmic Decrement using Circular Damping Coefficient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2))
δ = (2*pi*c)/(sqrt(cc^2-c^2))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Logarithmic Decrement - Logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Critical Damping Coefficient - (Measured in Newton Second per Meter) - Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator.
STEP 1: Convert Input(s) to Base Unit
Damping Coefficient: 0.8 Newton Second per Meter --> 0.8 Newton Second per Meter No Conversion Required
Critical Damping Coefficient: 8 Newton Second per Meter --> 8 Newton Second per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δ = (2*pi*c)/(sqrt(cc^2-c^2)) --> (2*pi*0.8)/(sqrt(8^2-0.8^2))
Evaluating ... ...
δ = 0.631483883399655
STEP 3: Convert Result to Output's Unit
0.631483883399655 --> No Conversion Required
FINAL ANSWER
0.631483883399655 0.631484 <-- Logarithmic Decrement
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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 using Circular Damping Coefficient Formula

Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2))
δ = (2*pi*c)/(sqrt(cc^2-c^2))

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 using Circular Damping Coefficient?

Logarithmic Decrement using Circular Damping Coefficient calculator uses Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2)) to calculate the Logarithmic Decrement, The Logarithmic Decrement using Circular Damping Coefficient 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 Circular Damping Coefficient using this online calculator? To use this online calculator for Logarithmic Decrement using Circular Damping Coefficient, enter Damping Coefficient (c) & Critical Damping Coefficient (cc) and hit the calculate button. Here is how the Logarithmic Decrement using Circular Damping Coefficient calculation can be explained with given input values -> 0.393468 = (2*pi*0.8)/(sqrt(8^2-0.8^2)).

FAQ

What is Logarithmic Decrement using Circular Damping Coefficient?
The Logarithmic Decrement using Circular Damping Coefficient formula is defined as the natural log of the ratio of the amplitudes of any two successive peaks and is represented as δ = (2*pi*c)/(sqrt(cc^2-c^2)) or Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2)). Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system & Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator.
How to calculate Logarithmic Decrement using Circular Damping Coefficient?
The Logarithmic Decrement using Circular Damping Coefficient formula is defined as the natural log of the ratio of the amplitudes of any two successive peaks is calculated using Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2)). To calculate Logarithmic Decrement using Circular Damping Coefficient, you need Damping Coefficient (c) & Critical Damping Coefficient (cc). With our tool, you need to enter the respective value for Damping Coefficient & Critical Damping Coefficient 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 Damping Coefficient & Critical Damping Coefficient. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Logarithmic Decrement = Frequency Constant for Calculation*Time Period
  • 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))
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