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Natural Frequency of Free Longitudinal Vibrations Formula

GoNatural Frequency of Free Longitudinal Vibrations given Static Deflection Formula

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Frequency is the number of oscillations or cycles per second of a free longitudinal vibration of an object or substance in a given time period. Check FAQs

f = \frac{\sqrt{\frac{g}{δ}}}{2 \cdot π}

f - Frequency?g - Acceleration due to Gravity?δ - Static Deflection?π - Archimedes' constant?

Natural Frequency of Free Longitudinal Vibrations Example

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Here is how the Natural Frequency of Free Longitudinal Vibrations equation looks like with Values.

Here is how the Natural Frequency of Free Longitudinal Vibrations equation looks like with Units.

Here is how the Natural Frequency of Free Longitudinal Vibrations equation looks like.

0.6351 = \frac{\sqrt{\frac{9.8}{0.6154}}}{2 \cdot 3.1416}

0.6351Hz = \frac{\sqrt{\frac{9.8m/s²}{0.6154m}}}{2 \cdot 3.1416}

0.6351 = \frac{\sqrt{\frac{9.8}{0.6154}}}{2 \cdot 3.1416}

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Natural Frequency of Free Longitudinal Vibrations Solution

Follow our step by step solution on how to calculate Natural Frequency of Free Longitudinal Vibrations?

FIRST Step Consider the formula

f = \frac{\sqrt{\frac{g}{δ}}}{2 \cdot π}

Next Step Substitute values of Variables

∴

f = \frac{\sqrt{\frac{9.8m/s²}{0.6154m}}}{2 \cdot π}

Next Step Substitute values of Constants

∴

f = \frac{\sqrt{\frac{9.8m/s²}{0.6154m}}}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

f = \frac{\sqrt{\frac{9.8}{0.6154}}}{2 \cdot 3.1416}

Next Step Evaluate

∴

f = 0.635125942335985Hz

LAST Step Rounding Answer

∴

f = 0.6351Hz

Natural Frequency of Free Longitudinal Vibrations Formula Elements

Variables

Constants

Functions

Frequency

Frequency is the number of oscillations or cycles per second of a free longitudinal vibration of an object or substance in a given time period.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

Acceleration due to Gravity

Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Static Deflection

Static Deflection is the maximum displacement of an object or structure under a given load, in the context of natural frequency of free longitudinal vibrations.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

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 to find Frequency

Go Natural Frequency of Free Longitudinal Vibrations given Static Deflection

f = \frac{0.4985}{\sqrt{δ}}

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 Natural Frequency of Free Longitudinal Vibrations?

Natural Frequency of Free Longitudinal Vibrations evaluator uses Frequency = (sqrt(Acceleration due to Gravity/Static Deflection))/(2*pi) to evaluate the Frequency, Natural Frequency of Free Longitudinal Vibrations formula is defined as a measure of the frequency at which a system vibrates freely when it is displaced from its equilibrium position and then released, characterizing the natural oscillation of a system in the longitudinal direction. Frequency is denoted by f symbol.

How to evaluate Natural Frequency of Free Longitudinal Vibrations using this online evaluator? To use this online evaluator for Natural Frequency of Free Longitudinal Vibrations, enter Acceleration due to Gravity (g) & Static Deflection (δ) and hit the calculate button.

FAQs on Natural Frequency of Free Longitudinal Vibrations

What is the formula to find Natural Frequency of Free Longitudinal Vibrations?

The formula of Natural Frequency of Free Longitudinal Vibrations is expressed as Frequency = (sqrt(Acceleration due to Gravity/Static Deflection))/(2*pi). Here is an example- 0.635126 = (sqrt(9.8/0.615384615))/(2*pi).

How to calculate Natural Frequency of Free Longitudinal Vibrations?

With Acceleration due to Gravity (g) & Static Deflection (δ) we can find Natural Frequency of Free Longitudinal Vibrations using the formula - Frequency = (sqrt(Acceleration due to Gravity/Static Deflection))/(2*pi). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Frequency?

Here are the different ways to Calculate Frequency-

Frequency=0.4985/(sqrt(Static Deflection))

Can the Natural Frequency of Free Longitudinal Vibrations be negative?

Yes, the Natural Frequency of Free Longitudinal Vibrations, measured in Frequency can be negative.

Which unit is used to measure Natural Frequency of Free Longitudinal Vibrations?

Natural Frequency of Free Longitudinal Vibrations is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Natural Frequency of Free Longitudinal Vibrations can be measured.

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