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Natural Frequency of Vibration Formula

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Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior. Check FAQs

f n = \frac{\sqrt{\frac{q}{I d}}}{2 \cdot π}

f_n - Natural Frequency?q - Torsional Stiffness?I_d - Mass Moment of Inertia of Disc?π - Archimedes' constant?

Natural Frequency of Vibration Example

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

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

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

0.1485 = \frac{\sqrt{\frac{5.4}{6.2}}}{2 \cdot 3.1416}

0.1485Hz = \frac{\sqrt{\frac{5.4N/m}{6.2kg·m²}}}{2 \cdot 3.1416}

0.1485 = \frac{\sqrt{\frac{5.4}{6.2}}}{2 \cdot 3.1416}

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Natural Frequency of Vibration Solution

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

FIRST Step Consider the formula

f n = \frac{\sqrt{\frac{q}{I d}}}{2 \cdot π}

Next Step Substitute values of Variables

∴

f n = \frac{\sqrt{\frac{5.4N/m}{6.2kg·m²}}}{2 \cdot π}

Next Step Substitute values of Constants

∴

f n = \frac{\sqrt{\frac{5.4N/m}{6.2kg·m²}}}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

f n = \frac{\sqrt{\frac{5.4}{6.2}}}{2 \cdot 3.1416}

Next Step Evaluate

∴

f n = 0.148532389167479Hz

LAST Step Rounding Answer

∴

f n = 0.1485Hz

Natural Frequency of Vibration Formula Elements

Variables

Constants

Functions

Natural Frequency

Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.

Symbol: f_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency

Torsional Stiffness

torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

Symbol: q

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Torsional Stiffness

Mass Moment of Inertia of Disc

Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.

Symbol: I_d

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Disc

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 Natural Frequency of Free Torsional Vibrations category

Go Moment of Inertia of Disc using Natural Frequency of Vibration

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

Go Torsional Stiffness of Shaft given Natural Frequency of Vibration

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

Go Moment of Inertia of Disc given Time Period of Vibration

I d = \frac{{t p}^{2} \cdot q}{{(2 \cdot π)}^{2}}

Go Torsional Stiffness of Shaft given Time Period of Vibration

q = \frac{{(2 \cdot π)}^{2} \cdot I d}{{(t p)}^{2}}

How to Evaluate Natural Frequency of Vibration?

Natural Frequency of Vibration evaluator uses Natural Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi) to evaluate the Natural Frequency, Natural Frequency of Vibration formula is defined as a measure of the number of oscillations per unit time of a torsional vibrational system, which is a critical parameter in the design and analysis of mechanical systems, particularly in the context of rotational motion and vibration. Natural Frequency is denoted by f_n symbol.

How to evaluate Natural Frequency of Vibration using this online evaluator? To use this online evaluator for Natural Frequency of Vibration, enter Torsional Stiffness (q) & Mass Moment of Inertia of Disc (I_d) and hit the calculate button.

FAQs on Natural Frequency of Vibration

What is the formula to find Natural Frequency of Vibration?

The formula of Natural Frequency of Vibration is expressed as Natural Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi). Here is an example- 0.148532 = (sqrt(5.4/6.2))/(2*pi).

How to calculate Natural Frequency of Vibration?

With Torsional Stiffness (q) & Mass Moment of Inertia of Disc (I_d) we can find Natural Frequency of Vibration using the formula - Natural Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Natural Frequency of Vibration be negative?

No, the Natural Frequency of Vibration, measured in Frequency cannot be negative.

Which unit is used to measure Natural Frequency of Vibration?

Natural Frequency of Vibration 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 Vibration can be measured.

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Natural Frequency of Vibration Formula

Natural Frequency of Vibration Example

Natural Frequency of Vibration Solution

Natural Frequency of Vibration Formula Elements

Other formulas in Natural Frequency of Free Torsional Vibrations category

How to Evaluate Natural Frequency of Vibration?

FAQs on Natural Frequency of Vibration

Variable Name