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Time Period of Free Transverse Vibrations Calculator

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General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%
✖Stiffness of Shaft is the measure of a shaft's resistance to bending or deformation during free transverse vibrations, affecting its natural frequency.ⓘ Stiffness of Shaft [s]			+10% -10%

✖Time Period is the duration of one cycle of free transverse vibrations of an object, characterizing its natural frequency of oscillation.ⓘ Time Period of Free Transverse Vibrations [t_p]

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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 duration of one cycle of free transverse vibrations of an object, characterizing its natural frequency of oscillation.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.
Stiffness of Shaft - (Measured in Newton per Meter) - Stiffness of Shaft is the measure of a shaft's resistance to bending or deformation during free transverse vibrations, affecting its natural frequency.

STEP 1: Convert Input(s) to Base Unit

Load Attached to Free End of Constraint: 0.453411 Kilogram --> 0.453411 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(0.453411/0.63)

Evaluating ... ...

t_p = 5.33034868933131

STEP 3: Convert Result to Output's Unit

5.33034868933131 Second --> No Conversion Required

FINAL ANSWER

5.33034868933131 ≈ 5.330349 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 Transverse Vibrations » Mechanical » General Shaft » Time Period of Free Transverse Vibrations

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National Institute Of Technology (NIT), Hamirpur

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< General Shaft 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)

Time Period of Free Transverse Vibrations Formula

LaTeX Go

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, Time Period of Free Transverse Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free transverse vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the object's dynamic behavior and stability. 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 -> 5.330349 = 2*pi*sqrt(0.453411/0.63).

FAQ

What is Time Period of Free Transverse Vibrations?

Time Period of Free Transverse Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free transverse vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the object's dynamic behavior and stability 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 the force applied to the free end of a constraint in a system undergoing free transverse vibrations & Stiffness of Shaft is the measure of a shaft's resistance to bending or deformation during free transverse vibrations, affecting its natural frequency.

How to calculate Time Period of Free Transverse Vibrations?

Time Period of Free Transverse Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle of free transverse vibration, which is a fundamental property of an object's natural frequency, and is crucial in understanding the object's dynamic behavior and stability 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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