Natural Frequency of Longitudinal Vibration Calculator

✖Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%
✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%
✖Total Mass of Constraint is both a property of a physical body and a measure of its resistance to acceleration.ⓘ Total Mass of Constraint [m_c]			+10% -10%

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

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Formula

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Natural Frequency of Longitudinal Vibration

Formula

`"f" = sqrt(("s"_{"constrain"})/("W"_{"attached"}+"m"_{"c"}/3))*1/(2*pi)`

Example

`"0.18281Hz"=sqrt(("13N/m")/("0.52kg"+"28kg"/3))*1/(2*pi)`

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Download Effect of Inertia of Constraint in Longitudinal and Transverse Vibrations Formulas PDF

Natural Frequency of Longitudinal Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi)
f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi)
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 Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Total Mass of Constraint - (Measured in Kilogram) - Total Mass of Constraint is both a property of a physical body and a measure of its resistance to acceleration.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required
Total Mass of Constraint: 28 Kilogram --> 28 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi) --> sqrt((13)/(0.52+28/3))*1/(2*pi)

Evaluating ... ...

f = 0.182810114343782

STEP 3: Convert Result to Output's Unit

0.182810114343782 Hertz --> No Conversion Required

FINAL ANSWER

0.182810114343782 ≈ 0.18281 Hertz <-- Frequency

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 6 Longitudinal Vibration Calculators

Natural Frequency of Longitudinal Vibration

Go Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi)

Velocity of Small Element for Longitudinal Vibration

Go Velocity of Small Element = (Distance between Small Element and Fixed End*Longitudinal Velocity of Free End)/Length of Constraint

Length of Constraint for Longitudinal Vibration

Go Length of Constraint = (Longitudinal Velocity of Free End*Distance between Small Element and Fixed End)/Velocity of Small Element

Longitudinal Velocity of Free End for Longitudinal Vibration

Go Longitudinal Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass of Constraint)

Total Mass of Constraint for Longitudinal Vibration

Go Total Mass of Constraint = (6*Kinetic Energy)/(Longitudinal Velocity of Free End^2)

Total Kinetic Energy of Constraint in Longitudinal Vibration

Go Kinetic Energy = (Total Mass of Constraint*Longitudinal Velocity of Free End^2)/6

Natural Frequency of Longitudinal Vibration Formula

Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi)
f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi)

What is longitudinal mode of vibration?

A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces.

How to Calculate Natural Frequency of Longitudinal Vibration?

Natural Frequency of Longitudinal Vibration calculator uses Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi) to calculate the Frequency, The Natural frequency of longitudinal vibration formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force. Frequency is denoted by f symbol.

How to calculate Natural Frequency of Longitudinal Vibration using this online calculator? To use this online calculator for Natural Frequency of Longitudinal Vibration, enter Stiffness of Constraint (s_constrain), Load Attached to Free End of Constraint (W_attached) & Total Mass of Constraint (m_c) and hit the calculate button. Here is how the Natural Frequency of Longitudinal Vibration calculation can be explained with given input values -> 0.18281 = sqrt((13)/(0.52+28/3))*1/(2*pi).

FAQ

What is Natural Frequency of Longitudinal Vibration?

The Natural frequency of longitudinal vibration formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force and is represented as f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi) or Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration, Load attached to free end of constraint is a weight or source of pressure & Total Mass of Constraint is both a property of a physical body and a measure of its resistance to acceleration.

How to calculate Natural Frequency of Longitudinal Vibration?

The Natural frequency of longitudinal vibration formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force is calculated using Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). To calculate Natural Frequency of Longitudinal Vibration, you need Stiffness of Constraint (s_constrain), Load Attached to Free End of Constraint (W_attached) & Total Mass of Constraint (m_c). With our tool, you need to enter the respective value for Stiffness of Constraint, Load Attached to Free End of Constraint & Total Mass of Constraint 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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