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Natural Frequency of Torsional Vibration System Formula

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Angular Frequency is the number of oscillations or cycles per unit time of a vibrating system, characterizing its mechanical vibration. Check FAQs

ω' = \sqrt{\frac{s}{I disc}}

ω' - Angular Frequency?s - Stiffness of Shaft?I_disc - Mass moment of inertia of disc?

Natural Frequency of Torsional Vibration System Example

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Here is how the Natural Frequency of Torsional Vibration System equation looks like with Values.

Here is how the Natural Frequency of Torsional Vibration System equation looks like with Units.

Here is how the Natural Frequency of Torsional Vibration System equation looks like.

2.0006 = \sqrt{\frac{0.63}{0.1574}}

2.0006rad/s = \sqrt{\frac{0.63N/m}{0.1574kg·m²}}

2.0006 = \sqrt{\frac{0.63}{0.1574}}

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Natural Frequency of Torsional Vibration System Solution

Follow our step by step solution on how to calculate Natural Frequency of Torsional Vibration System?

FIRST Step Consider the formula

ω' = \sqrt{\frac{s}{I disc}}

Next Step Substitute values of Variables

∴

ω' = \sqrt{\frac{0.63N/m}{0.1574kg·m²}}

Next Step Prepare to Evaluate

∴

ω' = \sqrt{\frac{0.63}{0.1574}}

Next Step Evaluate

∴

ω' = 2.00063522313814rad/s

LAST Step Rounding Answer

∴

ω' = 2.0006rad/s

Natural Frequency of Torsional Vibration System Formula Elements

Variables

Functions

Angular Frequency

Angular Frequency is the number of oscillations or cycles per unit time of a vibrating system, characterizing its mechanical vibration.

Symbol: ω'

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Frequency

Stiffness of Shaft

Stiffness of Shaft is the measure of a shaft's resistance to deformation or bending under an applied load in mechanical vibration systems.

Symbol: s

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Shaft

Mass moment of inertia of disc

Mass moment of inertia of disc is a measure of an object's resistance to changes in its rotation rate in mechanical vibrations.

Symbol: I_disc

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass moment of inertia of disc

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 Undamped Free Vibration category

Go Equivalent Stiffness of Two Springs in Parallel

K eq = K 1 + K 2

Go Equivalent Stiffness of Two Springs in Series

K eq = \frac{K 1 \cdot K 2}{K 1 + K 2}

Go Frequency of Vibration

v vib = \frac{1}{2 \cdot π} \cdot \sqrt{\frac{k 1}{m}}

How to Evaluate Natural Frequency of Torsional Vibration System?

Natural Frequency of Torsional Vibration System evaluator uses Angular Frequency = sqrt(Stiffness of Shaft/Mass moment of inertia of disc) to evaluate the Angular Frequency, Natural Frequency of Torsional Vibration System formula is defined as a measure of the frequency at which a torsional vibration system tends to oscillate when it is subjected to an external torque, providing valuable insights into the dynamic behavior of mechanical systems. Angular Frequency is denoted by ω' symbol.

How to evaluate Natural Frequency of Torsional Vibration System using this online evaluator? To use this online evaluator for Natural Frequency of Torsional Vibration System, enter Stiffness of Shaft (s) & Mass moment of inertia of disc (I_disc) and hit the calculate button.

FAQs on Natural Frequency of Torsional Vibration System

What is the formula to find Natural Frequency of Torsional Vibration System?

The formula of Natural Frequency of Torsional Vibration System is expressed as Angular Frequency = sqrt(Stiffness of Shaft/Mass moment of inertia of disc). Here is an example- 0.318768 = sqrt(0.63/0.1574).

How to calculate Natural Frequency of Torsional Vibration System?

With Stiffness of Shaft (s) & Mass moment of inertia of disc (I_disc) we can find Natural Frequency of Torsional Vibration System using the formula - Angular Frequency = sqrt(Stiffness of Shaft/Mass moment of inertia of disc). This formula also uses Square Root (sqrt) function(s).

Can the Natural Frequency of Torsional Vibration System be negative?

Yes, the Natural Frequency of Torsional Vibration System, measured in Angular Frequency can be negative.

Which unit is used to measure Natural Frequency of Torsional Vibration System?

Natural Frequency of Torsional Vibration System is usually measured using the Radian per Second[rad/s] for Angular Frequency. Degree per Second[rad/s] are the few other units in which Natural Frequency of Torsional Vibration System can be measured.

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