Angular Velocity of Free Longitudinal Vibrations Calculator

✖Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.ⓘ Stiffness of Constraint [s_constrain]			+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.ⓘ Angular Velocity of Free Longitudinal Vibrations [ω_n]

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Formula

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Angular Velocity of Free Longitudinal Vibrations

Formula

`"ω"_{"n"} = sqrt("s"_{"constrain"}/"m")`

Example

`"7.211103rad/s"=sqrt("13N/m"/".25kg")`

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Download Natural Frequency of Free Longitudinal Vibrations Formula PDF

Angular Velocity of Free Longitudinal Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring)
ω_n = sqrt(s_constrain/m)
This formula uses 1 Functions, 3 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

Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.
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.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
Mass suspended from spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = sqrt(s_constrain/m) --> sqrt(13/0.25)

Evaluating ... ...

ω_n = 7.21110255092798

STEP 3: Convert Result to Output's Unit

7.21110255092798 Radian per Second --> No Conversion Required

FINAL ANSWER

7.21110255092798 ≈ 7.211103 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Longitudinal Vibrations » Equilibrium Method » Angular Velocity of Free Longitudinal Vibrations

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National Institute Of Technology (NIT), Hamirpur

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< 12 Equilibrium Method Calculators

Load Attached to Free End of Constraint

Go Weight of Body in Newtons = (Static Deflection*Young's Modulus*Cross Sectional Area)/Length of Constraint

Length of Constraint

Go Length of Constraint = (Static Deflection*Young's Modulus*Cross Sectional Area)/Weight of Body in Newtons

Restoring Force using Weight of Body

Go Force = Weight of Body in Newtons-Stiffness of Constraint*(Static Deflection+Displacement of Body)

Acceleration of Body given Stiffness of Constraint

Go Acceleration of Body = (-Stiffness of Constraint*Displacement of Body)/Load Attached to Free End of Constraint

Displacement of Body given Stiffness of Constraint

Go Displacement of Body = (-Load Attached to Free End of Constraint*Acceleration of Body)/Stiffness of Constraint

Time Period of Free Longitudinal Vibrations

Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)

Angular Velocity of Free Longitudinal Vibrations

Go Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring)

Critical Damping Coefficient given Spring Constant

Go Critical Damping Coefficient = 2*sqrt(Spring Constant/Mass suspended from spring)

Static Deflection given Natural Frequency

Go Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2)

Gravitational Pull Balanced by Spring Force

Go Weight of Body in Newtons = Stiffness of Constraint*Static Deflection

Restoring Force

Go Force = -Stiffness of Constraint*Displacement of Body

Young's Modulus

Go Young's Modulus = Stress/Strain

Angular Velocity of Free Longitudinal Vibrations Formula

Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring)
ω_n = sqrt(s_constrain/m)

What is difference between longitudinal and transverse wave?

Transverse waves are always characterized by particle motion being perpendicular to wave motion. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves.

How to Calculate Angular Velocity of Free Longitudinal Vibrations?

Angular Velocity of Free Longitudinal Vibrations calculator uses Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring) to calculate the Natural Circular Frequency, The Angular velocity of free longitudinal vibrations formula is defined the square root of the ratio of stiffness constant and mass of the body. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Angular Velocity of Free Longitudinal Vibrations using this online calculator? To use this online calculator for Angular Velocity of Free Longitudinal Vibrations, enter Stiffness of Constraint (s_constrain) & Mass suspended from spring (m) and hit the calculate button. Here is how the Angular Velocity of Free Longitudinal Vibrations calculation can be explained with given input values -> 7.211103 = sqrt(13/0.25).

FAQ

What is Angular Velocity of Free Longitudinal Vibrations?

The Angular velocity of free longitudinal vibrations formula is defined the square root of the ratio of stiffness constant and mass of the body and is represented as ω_n = sqrt(s_constrain/m) or Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring). Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration & A mass suspended from spring is defined as the quantitative measure of inertia, a fundamental property of all matter.

How to calculate Angular Velocity of Free Longitudinal Vibrations?

The Angular velocity of free longitudinal vibrations formula is defined the square root of the ratio of stiffness constant and mass of the body is calculated using Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring). To calculate Angular Velocity of Free Longitudinal Vibrations, you need Stiffness of Constraint (s_constrain) & Mass suspended from spring (m). With our tool, you need to enter the respective value for Stiffness of Constraint & Mass suspended from spring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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