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Time Period of Free Longitudinal Vibrations Formula

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Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency. Check FAQs

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

t_p - Time Period?m - Mass of Body?s_constrain - Stiffness of Constraint?π - Archimedes' constant?

Time Period of Free Longitudinal Vibrations Example

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

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

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

0.2993 = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.0295}{13}}

0.2993s = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.0295N}{13N/m}}

0.2993 = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.0295}{13}}

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Time Period of Free Longitudinal Vibrations Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t p = 2 \cdot π \cdot \sqrt{\frac{0.0295N}{13N/m}}

Next Step Substitute values of Constants

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.0295N}{13N/m}}

Next Step Prepare to Evaluate

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{0.0295}{13}}

Next Step Evaluate

∴

t p = 0.29930860319802s

LAST Step Rounding Answer

∴

t p = 0.2993s

Time Period of Free Longitudinal Vibrations Formula Elements

Variables

Constants

Functions

Time Period

Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period

Mass of Body

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.

Symbol: m

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Mass of Body

Stiffness of Constraint

Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

Symbol: s_constrain

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Constraint

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 Equilibrium Method category

Go Gravitational Pull Balanced by Spring Force

W = s constrain \cdot δ

Go Restoring Force

F re = - s constrain \cdot s body

Go Acceleration of Body given Stiffness of Constraint

a = \frac{s constrain \cdot s body}{W attached}

Go Displacement of Body given Stiffness of Constraint

s body = \frac{W attached \cdot a}{s constrain}

How to Evaluate Time Period of Free Longitudinal Vibrations?

Time Period of Free Longitudinal Vibrations evaluator uses Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint) to evaluate 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 evaluate Time Period of Free Longitudinal Vibrations using this online evaluator? To use this online evaluator for Time Period of Free Longitudinal Vibrations, enter Mass of Body (m) & Stiffness of Constraint (s_constrain) and hit the calculate button.

FAQs on Time Period of Free Longitudinal Vibrations

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

The formula of Time Period of Free Longitudinal Vibrations is expressed as Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint). Here is an example- 4.928936 = 2*pi*sqrt(0.0295/13).

How to calculate Time Period of Free Longitudinal Vibrations?

With Mass of Body (m) & Stiffness of Constraint (s_constrain) we can find Time Period of Free Longitudinal Vibrations using the formula - Time Period = 2*pi*sqrt(Mass of Body/Stiffness of Constraint). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Time Period of Free Longitudinal Vibrations be negative?

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

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

Time Period of Free Longitudinal 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 Longitudinal Vibrations can be measured.

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Time Period of Free Longitudinal Vibrations Formula

Time Period of Free Longitudinal Vibrations Example

Time Period of Free Longitudinal Vibrations Solution

Time Period of Free Longitudinal Vibrations Formula Elements

Other formulas in Equilibrium Method category

How to Evaluate Time Period of Free Longitudinal Vibrations?

FAQs on Time Period of Free Longitudinal Vibrations

Variable Name