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Time Period of Free Longitudinal Vibrations Calculator

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Natural Frequency

✖Weight of Body in Newtons is the force with which a body is pulled toward the earth.ⓘ Weight of Body in Newtons [W]			+10% -10%
✖Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%

✖Time Period is the time taken by a complete cycle of the wave to pass a point.ⓘ Time Period of Free Longitudinal Vibrations [t_p]

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Formula

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Time Period of Free Longitudinal Vibrations

Formula

t p = 2 \cdot π \cdot \sqrt{\frac{W}{s constrain}}

Example

4.928936 s = 2 \cdot π \cdot \sqrt{\frac{8 N}{13 N/m}}

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Download Natural Frequency of Free Longitudinal Vibrations Formula PDF PDF Image

Time Period of Free Longitudinal Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)
t_p = 2*pi*sqrt(W/s_constrain)
This formula uses 1 Constants, 1 Functions, 3 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

Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
Weight of Body in Newtons - (Measured in Newton) - Weight of Body in Newtons is the force with which a body is pulled toward the earth.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.

STEP 1: Convert Input(s) to Base Unit

Weight of Body in Newtons: 8 Newton --> 8 Newton No Conversion Required
Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = 2*pi*sqrt(W/s_constrain) --> 2*pi*sqrt(8/13)

Evaluating ... ...

t_p = 4.92893607520434

STEP 3: Convert Result to Output's Unit

4.92893607520434 Second --> No Conversion Required

FINAL ANSWER

4.92893607520434 ≈ 4.928936 Second <-- Time Period

(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 » Mechanical » Equilibrium Method » Time Period of Free Longitudinal Vibrations

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National Institute Of Technology (NIT), Hamirpur

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< Equilibrium Method Calculators

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

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

< Rayleigh’s Method Calculators

Velocity at Mean Position

Go Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)

Maximum Kinetic Energy at Mean Position

Go Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2

Maximum Potential Energy at Mean Position

Go Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2

Maximum Velocity at Mean Position by Rayleigh Method

Go Maximum Velocity = Cumulative Frequency*Maximum Displacement

Time Period of Free Longitudinal Vibrations Formula

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

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 Time Period of Free Longitudinal Vibrations?

Time Period of Free Longitudinal Vibrations calculator uses Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint) to calculate the Time Period, The Time period of free longitudinal vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point. Time Period is denoted by t_p symbol.

How to calculate Time Period of Free Longitudinal Vibrations using this online calculator? To use this online calculator for Time Period of Free Longitudinal Vibrations, enter Weight of Body in Newtons (W) & Stiffness of Constraint (s_constrain) and hit the calculate button. Here is how the Time Period of Free Longitudinal Vibrations calculation can be explained with given input values -> 4.928936 = 2*pi*sqrt(8/13).

FAQ

What is Time Period of Free Longitudinal Vibrations?

The Time period of free longitudinal vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point and is represented as t_p = 2*pi*sqrt(W/s_constrain) or Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint). Weight of Body in Newtons is the force with which a body is pulled toward the earth & Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.

How to calculate Time Period of Free Longitudinal Vibrations?

The Time period of free longitudinal vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point is calculated using Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint). To calculate Time Period of Free Longitudinal Vibrations, you need Weight of Body in Newtons (W) & Stiffness of Constraint (s_constrain). With our tool, you need to enter the respective value for Weight of Body in Newtons & Stiffness of Constraint 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 Time Period?

In this formula, Time Period uses Weight of Body in Newtons & Stiffness of Constraint. We can use 1 other way(s) to calculate the same, which is/are as follows -

Time Period = (2*pi)/Natural Circular Frequency

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