Damping Factor given Natural Frequency Calculator

✖Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.ⓘ Damping Coefficient [c]			+10% -10%
✖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%

✖Damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.ⓘ Damping Factor given Natural Frequency [ζ]

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Formula

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Damping Factor given Natural Frequency

Formula

`"ζ" = "c"/(2*"m"*"ω"_{"n"})`

Example

`"0.015238"="0.8Ns/m"/(2*"1.25kg"*"21rad/s")`

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Damping Factor given Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)
ζ = c/(2*m*ω_n)
This formula uses 4 Variables

Variables Used

Damping Ratio - Damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.
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.
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

Damping Coefficient: 0.8 Newton Second per Meter --> 0.8 Newton Second per Meter No Conversion Required
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

ζ = c/(2*m*ω_n) --> 0.8/(2*1.25*21)

Evaluating ... ...

ζ = 0.0152380952380952

STEP 3: Convert Result to Output's Unit

0.0152380952380952 --> No Conversion Required

FINAL ANSWER

0.0152380952380952 ≈ 0.015238 <-- Damping Ratio

(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 » Damping Factor given Natural Frequency

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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

Damping Factor given Natural Frequency Formula

Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)
ζ = 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 Damping Factor given Natural Frequency?

Damping Factor given Natural Frequency calculator uses Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency) to calculate the Damping Ratio, Damping Factor given Natural Frequency is defined as the ratio of the rated impedance of the loudspeaker to the source impedance. Damping Ratio is denoted by ζ symbol.

How to calculate Damping Factor given Natural Frequency using this online calculator? To use this online calculator for Damping Factor given Natural Frequency, enter Damping Coefficient (c), Mass Suspended from Spring (m) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Damping Factor given Natural Frequency calculation can be explained with given input values -> 0.07619 = 0.8/(2*1.25*21).

FAQ

What is Damping Factor given Natural Frequency?

Damping Factor given Natural Frequency is defined as the ratio of the rated impedance of the loudspeaker to the source impedance and is represented as ζ = c/(2*m*ω_n) or Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency). Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system, 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 Damping Factor given Natural Frequency?

Damping Factor given Natural Frequency is defined as the ratio of the rated impedance of the loudspeaker to the source impedance is calculated using Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency). To calculate Damping Factor given Natural Frequency, you need Damping Coefficient (c), Mass Suspended from Spring (m) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Damping Coefficient, 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 Damping Ratio?

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

Damping Ratio = Damping Coefficient/Critical Damping Coefficient

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