Frequency of Damped Vibration Calculator

✖Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.ⓘ Stiffness of Spring [k]			+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%
✖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%

✖Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.ⓘ Frequency of Damped Vibration [f]

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Formula

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Frequency of Damped Vibration

Formula

`"f" = 1/(2*pi)*sqrt("k"/"m"-("c"/(2*"m"))^2)`

Example

`"1.101481Hz"=1/(2*pi)*sqrt("60N/m"/"1.25kg"-("0.8Ns/m"/(2*"1.25kg"))^2)`

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Download Frequency of Free Damped Vibrations Formulas PDF

Frequency of Damped Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)
f = 1/(2*pi)*sqrt(k/m-(c/(2*m))^2)
This formula uses 1 Constants, 1 Functions, 4 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

Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Mass Suspended from Spring: 1.25 Kilogram --> 1.25 Kilogram No Conversion Required
Damping Coefficient: 0.8 Newton Second per Meter --> 0.8 Newton Second per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = 1/(2*pi)*sqrt(k/m-(c/(2*m))^2) --> 1/(2*pi)*sqrt(60/1.25-(0.8/(2*1.25))^2)

Evaluating ... ...

f = 1.10148099457358

STEP 3: Convert Result to Output's Unit

1.10148099457358 Hertz --> No Conversion Required

FINAL ANSWER

1.10148099457358 ≈ 1.101481 Hertz <-- Frequency

(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 » Under Damping » Frequency of Damped Vibration

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 10+ Under Damping Calculators

Periodic Time of Vibration

Go Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2))

Frequency of Damped Vibration

Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)

Circular Damped Frequency

Go Circular Damped Frequency = sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)

Periodic Time of Vibration using Natural Frequency

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

Frequency of Damped Vibration using Natural Frequency

Go Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)

Displacement of Mass from Mean Position

Go Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period)

Frequency of Undamped Vibration

Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Frequency Constant for Damped Vibrations given Circular Frequency

Go Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2)

Circular Damped Frequency given Natural Frequency

Go Circular Damped Frequency = sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)

Frequency Constant for Damped Vibrations

Go Frequency Constant for Calculation = Damping Coefficient/Mass Suspended from Spring

Frequency of Damped Vibration Formula

Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)
f = 1/(2*pi)*sqrt(k/m-(c/(2*m))^2)

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 Frequency of Damped Vibration?

Frequency of Damped Vibration calculator uses Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2) to calculate the Frequency, The Frequency of damped vibration is defined as the absorption of the energy of oscillations, by whatever means. Generally, this results in the decreased amplitude of the waves. The processes which result in damping also reduce the natural frequency of a system. Frequency is denoted by f symbol.

How to calculate Frequency of Damped Vibration using this online calculator? To use this online calculator for Frequency of Damped Vibration, enter Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) and hit the calculate button. Here is how the Frequency of Damped Vibration calculation can be explained with given input values -> 1.101481 = 1/(2*pi)*sqrt(60/1.25-(0.8/(2*1.25))^2).

FAQ

What is Frequency of Damped Vibration?

The Frequency of damped vibration is defined as the absorption of the energy of oscillations, by whatever means. Generally, this results in the decreased amplitude of the waves. The processes which result in damping also reduce the natural frequency of a system and is represented as f = 1/(2*pi)*sqrt(k/m-(c/(2*m))^2) or Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2). Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness, A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter & Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

How to calculate Frequency of Damped Vibration?

The Frequency of damped vibration is defined as the absorption of the energy of oscillations, by whatever means. Generally, this results in the decreased amplitude of the waves. The processes which result in damping also reduce the natural frequency of a system is calculated using Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2). To calculate Frequency of Damped Vibration, you need Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c). With our tool, you need to enter the respective value for Stiffness of Spring, Mass Suspended from Spring & 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 Frequency?

In this formula, Frequency uses Stiffness of Spring, Mass Suspended from Spring & Damping Coefficient. We can use 2 other way(s) to calculate the same, which is/are as follows -

Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)

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