Circular Damped Frequency 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%

✖Circular Damped Frequency refers to the angular displacement per unit time.ⓘ Circular Damped Frequency [ω_d]

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Formula

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Circular Damped Frequency

Formula

`"ω"_{"d"} = sqrt("k"/"m"-("c"/(2*"m"))^2)`

Example

`"6.920809"=sqrt("60N/m"/"1.25kg"-("0.8Ns/m"/(2*"1.25kg"))^2)`

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Download Frequency of Free Damped Vibrations Formulas PDF

Circular Damped Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Circular Damped Frequency - Circular Damped Frequency refers to the angular displacement per unit time.
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

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

Evaluating ... ...

ω_d = 6.92080920124229

STEP 3: Convert Result to Output's Unit

6.92080920124229 --> No Conversion Required

FINAL ANSWER

6.92080920124229 ≈ 6.920809 <-- Circular Damped 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 » Circular Damped Frequency

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National Institute Of Technology (NIT), Hamirpur

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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

Circular Damped Frequency Formula

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

Circular Damped Frequency calculator uses Circular Damped Frequency = sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2) to calculate the Circular Damped Frequency, The Circular damped frequency formula 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. Circular Damped Frequency is denoted by ω_d symbol.

How to calculate Circular Damped Frequency using this online calculator? To use this online calculator for Circular Damped Frequency, enter Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) and hit the calculate button. Here is how the Circular Damped Frequency calculation can be explained with given input values -> 15.40909 = sqrt(60/1.25-(0.8/(2*1.25))^2).

FAQ

What is Circular Damped Frequency?

The Circular damped frequency formula 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 ω_d = sqrt(k/m-(c/(2*m))^2) or Circular Damped Frequency = 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 Circular Damped Frequency?

The Circular damped frequency formula 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 Circular Damped Frequency = sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2). To calculate Circular Damped Frequency, 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 Circular Damped Frequency?

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

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

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