Time Period of Free Transverse Vibrations Calculator

✖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%
✖Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.ⓘ Stiffness of Shaft [s]			+10% -10%

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

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Formula

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Time Period of Free Transverse Vibrations

Formula

`"t"_{"p"} = 2*pi*sqrt("W"_{"attached"}/"s")`

Example

`"5.708359s"=2*pi*sqrt("0.52kg"/"0.63N/m")`

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Download Longitudinal and Transverse Vibrations Formula PDF

Time Period of Free Transverse Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)
t_p = 2*pi*sqrt(W_attached/s)
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.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Stiffness of Shaft - (Measured in Newton per Meter) - Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.

STEP 1: Convert Input(s) to Base Unit

Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required
Stiffness of Shaft: 0.63 Newton per Meter --> 0.63 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = 2*pi*sqrt(W_attached/s) --> 2*pi*sqrt(0.52/0.63)

Evaluating ... ...

t_p = 5.70835883265293

STEP 3: Convert Result to Output's Unit

5.70835883265293 Second --> No Conversion Required

FINAL ANSWER

5.70835883265293 ≈ 5.708359 Second <-- Time Period

(Calculation completed in 00.007 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Time Period of Free Transverse Vibrations

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 8 Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft

Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Natural Frequency of Free Transverse Vibrations

Go Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi

Time Period of Free Transverse Vibrations

Go Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)

Acceleration of Body given Stiffness of Shaft

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

Restoring Force using Stiffness of Shaft

Go Force = -Stiffness of Shaft*Displacement of Body

Time Period of Free Transverse Vibrations Formula

Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)
t_p = 2*pi*sqrt(W_attached/s)

What is the difference between a longitudinal and transverse waves?

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 Transverse Vibrations?

Time Period of Free Transverse Vibrations calculator uses Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft) to calculate the Time Period, The Time period of free transverse vibrations formula is defined as time period is 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 Transverse Vibrations using this online calculator? To use this online calculator for Time Period of Free Transverse Vibrations, enter Load Attached to Free End of Constraint (W_attached) & Stiffness of Shaft (s) and hit the calculate button. Here is how the Time Period of Free Transverse Vibrations calculation can be explained with given input values -> 5.708359 = 2*pi*sqrt(0.52/0.63).

FAQ

What is Time Period of Free Transverse Vibrations?

The Time period of free transverse vibrations formula is defined as time period is the time taken by a complete cycle of the wave to pass a point and is represented as t_p = 2*pi*sqrt(W_attached/s) or Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft). Load attached to free end of constraint is a weight or source of pressure & Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.

How to calculate Time Period of Free Transverse Vibrations?

The Time period of free transverse vibrations formula is defined as time period is the time taken by a complete cycle of the wave to pass a point is calculated using Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft). To calculate Time Period of Free Transverse Vibrations, you need Load Attached to Free End of Constraint (W_attached) & Stiffness of Shaft (s). With our tool, you need to enter the respective value for Load Attached to Free End of Constraint & Stiffness of Shaft 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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