Time Period of Free Longitudinal Vibrations Calculator

✖Mass of Body is the quantity of matter in an object, used to calculate the natural frequency of free longitudinal vibrations in a mechanical system.ⓘ Mass of Body [m]			+10% -10%
✖Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%

✖Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.ⓘ Time Period of Free Longitudinal Vibrations [t_p]

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Time Period of Free Longitudinal Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint)
t_p = 2*pi*sqrt(m/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 duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.
Mass of Body - (Measured in Newton) - Mass of Body is the quantity of matter in an object, used to calculate the natural frequency of free longitudinal vibrations in a mechanical system.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

STEP 1: Convert Input(s) to Base Unit

Mass of Body: 0.0295 Newton --> 0.0295 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(m/s_constrain) --> 2*pi*sqrt(0.0295/13)

Evaluating ... ...

t_p = 0.29930860319802

STEP 3: Convert Result to Output's Unit

0.29930860319802 Second --> No Conversion Required

FINAL ANSWER

0.29930860319802 ≈ 0.299309 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

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

Displacement of Body given Stiffness of Constraint

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

Gravitational Pull Balanced by Spring Force

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

Restoring Force

LaTeX Go Restoring Force = -Stiffness of Constraint*Displacement of Body

Time Period of Free Longitudinal Vibrations Formula

LaTeX Go

Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint)
t_p = 2*pi*sqrt(m/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(Mass of Body/Stiffness of Constraint) to calculate the Time Period, Time Period of Free Longitudinal Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free longitudinal vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the behavior of vibrating systems. 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 Mass of Body (m) & 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(0.0295/13).

FAQ

What is Time Period of Free Longitudinal Vibrations?

Time Period of Free Longitudinal Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free longitudinal vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the behavior of vibrating systems and is represented as t_p = 2*pi*sqrt(m/s_constrain) or Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint). Mass of Body is the quantity of matter in an object, used to calculate the natural frequency of free longitudinal vibrations in a mechanical system & Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

How to calculate Time Period of Free Longitudinal Vibrations?

Time Period of Free Longitudinal Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free longitudinal vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the behavior of vibrating systems is calculated using Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint). To calculate Time Period of Free Longitudinal Vibrations, you need Mass of Body (m) & Stiffness of Constraint (s_constrain). With our tool, you need to enter the respective value for Mass of Body & Stiffness 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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