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Time Period of Free Transverse Vibrations Formula

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Time Period is the duration of one cycle of free transverse vibrations of an object, characterizing its natural frequency of oscillation. Check FAQs

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

t_p - Time Period?W_attached - Load Attached to Free End of Constraint?s - Stiffness of Shaft?π - Archimedes' constant?

Time Period of Free Transverse Vibrations Example

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Here is how the Time Period of Free Transverse Vibrations equation looks like with Values.

Here is how the Time Period of Free Transverse Vibrations equation looks like with Units.

Here is how the Time Period of Free Transverse Vibrations equation looks like.

5.3303 = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.4534}{0.63}}

5.3303s = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.4534kg}{0.63N/m}}

5.3303 = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.4534}{0.63}}

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Time Period of Free Transverse Vibrations Solution

Follow our step by step solution on how to calculate Time Period of Free Transverse Vibrations?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t p = 2 \cdot π \cdot \sqrt{\frac{0.4534kg}{0.63N/m}}

Next Step Substitute values of Constants

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.4534kg}{0.63N/m}}

Next Step Prepare to Evaluate

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.4534}{0.63}}

Next Step Evaluate

∴

t p = 5.33034868933131s

LAST Step Rounding Answer

∴

t p = 5.3303s

Time Period of Free Transverse Vibrations Formula Elements

Variables

Constants

Functions

Time Period

Time Period is the duration of one cycle of free transverse vibrations of an object, characterizing its natural frequency of oscillation.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period

Load Attached to Free End of Constraint

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.

Symbol: W_attached

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

Stiffness of Shaft

Stiffness of Shaft is the measure of a shaft's resistance to bending or deformation during free transverse vibrations, affecting its natural frequency.

Symbol: s

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in General Shaft category

Go Static Deflection given Moment of Inertia of Shaft

δ = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot I shaft}

Go Load at Free End in Free Transverse Vibrations

W attached = \frac{δ \cdot 3 \cdot E \cdot I shaft}{{L shaft}^{3}}

Go Length of Shaft

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{3}}

Go Moment of Inertia of Shaft given Static Deflection

I shaft = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot δ}

How to Evaluate Time Period of Free Transverse Vibrations?

Time Period of Free Transverse Vibrations evaluator uses Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft) to evaluate 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 evaluate Time Period of Free Transverse Vibrations using this online evaluator? To use this online evaluator 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.

FAQs on Time Period of Free Transverse Vibrations

What is the formula to find Time Period of Free Transverse Vibrations?

The formula of Time Period of Free Transverse Vibrations is expressed as Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft). Here is an example- 5.330349 = 2*pi*sqrt(0.453411/0.63).

How to calculate Time Period of Free Transverse Vibrations?

With Load Attached to Free End of Constraint (W_attached) & Stiffness of Shaft (s) we can find Time Period of Free Transverse Vibrations using the formula - Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Time Period of Free Transverse Vibrations be negative?

No, the Time Period of Free Transverse Vibrations, measured in Time cannot be negative.

Which unit is used to measure Time Period of Free Transverse Vibrations?

Time Period of Free Transverse Vibrations is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Period of Free Transverse Vibrations can be measured.

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Time Period of Free Transverse Vibrations Formula

Time Period of Free Transverse Vibrations Example

Time Period of Free Transverse Vibrations Solution

Time Period of Free Transverse Vibrations Formula Elements

Other formulas in General Shaft category

How to Evaluate Time Period of Free Transverse Vibrations?

FAQs on Time Period of Free Transverse Vibrations

Variable Name