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Natural Frequency of Free Transverse Vibrations Formula

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Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior. Check FAQs

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

f - Frequency?s - Stiffness of Shaft?W_attached - Load Attached to Free End of Constraint?π - Archimedes' constant?

Natural Frequency of Free Transverse Vibrations Example

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

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

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

1.8516 = \frac{\sqrt{\frac{0.63}{0.4534}}}{2} \cdot 3.1416

1.8516Hz = \frac{\sqrt{\frac{0.63N/m}{0.4534kg}}}{2} \cdot 3.1416

1.8516 = \frac{\sqrt{\frac{0.63}{0.4534}}}{2} \cdot 3.1416

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Natural Frequency of Free Transverse Vibrations Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

f = 1.85158701171714Hz

LAST Step Rounding Answer

∴

f = 1.8516Hz

Natural Frequency of Free Transverse Vibrations Formula Elements

Variables

Constants

Functions

Frequency

Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

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

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

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 Natural Frequency of Free Transverse Vibrations?

Natural Frequency of Free Transverse Vibrations evaluator uses Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi to evaluate the Frequency, Natural Frequency of Free Transverse Vibrations formula is defined as a measure of the frequency at which a system vibrates freely in the transverse direction, typically in mechanical systems, and is influenced by the stiffness of the system and the weight of the attached load. Frequency is denoted by f symbol.

How to evaluate Natural Frequency of Free Transverse Vibrations using this online evaluator? To use this online evaluator for Natural Frequency of Free Transverse Vibrations, enter Stiffness of Shaft (s) & Load Attached to Free End of Constraint (W_attached) and hit the calculate button.

FAQs on Natural Frequency of Free Transverse Vibrations

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

The formula of Natural Frequency of Free Transverse Vibrations is expressed as Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi. Here is an example- 1.851587 = (sqrt(0.63/0.453411))/2*pi.

How to calculate Natural Frequency of Free Transverse Vibrations?

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

Can the Natural Frequency of Free Transverse Vibrations be negative?

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

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

Natural Frequency of Free Transverse 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 Transverse Vibrations can be measured.

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