Critical Damping Coefficient Calculator

✖A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.ⓘ Mass Suspended from Spring [m]			+10% -10%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator.ⓘ Critical Damping Coefficient [c_c]

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Formula

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Critical Damping Coefficient

Formula

`"c"_{"c"} = 2*"m"*"ω"_{"n"}`

Example

`"52.5Ns/m"=2*"1.25kg"*"21rad/s"`

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Download Frequency of Free Damped Vibrations Formulas PDF

Critical Damping Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency
c_c = 2*m*ω_n
This formula uses 3 Variables

Variables Used

Critical Damping Coefficient - (Measured in Newton Second per Meter) - Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator.
Mass Suspended from Spring - (Measured in Kilogram) - A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.

STEP 1: Convert Input(s) to Base Unit

Mass Suspended from Spring: 1.25 Kilogram --> 1.25 Kilogram No Conversion Required
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c_c = 2*m*ω_n --> 2*1.25*21

Evaluating ... ...

c_c = 52.5

STEP 3: Convert Result to Output's Unit

52.5 Newton Second per Meter --> No Conversion Required

FINAL ANSWER

52.5 Newton Second per Meter <-- Critical Damping Coefficient

(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 » Critical Damping Coefficient

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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

Critical Damping Coefficient Formula

Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency
c_c = 2*m*ω_n

Why damping happens during vibration?

The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness. Damped vibration happens when the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped.

How to Calculate Critical Damping Coefficient?

Critical Damping Coefficient calculator uses Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency to calculate the Critical Damping Coefficient, The Critical damping coefficient formula is defined as the quickest approach to zero amplitude for a damped oscillator. Critical Damping Coefficient is denoted by c_c symbol.

How to calculate Critical Damping Coefficient using this online calculator? To use this online calculator for Critical Damping Coefficient, enter Mass Suspended from Spring (m) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Critical Damping Coefficient calculation can be explained with given input values -> 10.5 = 2*1.25*21.

FAQ

What is Critical Damping Coefficient?

The Critical damping coefficient formula is defined as the quickest approach to zero amplitude for a damped oscillator and is represented as c_c = 2*m*ω_n or Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency. A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter & Natural Circular Frequency is a scalar measure of rotation rate.

How to calculate Critical Damping Coefficient?

The Critical damping coefficient formula is defined as the quickest approach to zero amplitude for a damped oscillator is calculated using Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency. To calculate Critical Damping Coefficient, you need Mass Suspended from Spring (m) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Mass Suspended from Spring & Natural Circular Frequency 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 Critical Damping Coefficient?

In this formula, Critical Damping Coefficient uses Mass Suspended from Spring & Natural Circular Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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