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Circular Frequency due to Uniformly Distributed Load Formula

GoCircular Frequency given Static Deflection Formula

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Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force. Check FAQs

ω n = π^{2} \cdot \sqrt{\frac{E \cdot I shaft \cdot g}{w \cdot {L shaft}^{4}}}

ω_n - Natural Circular Frequency?E - Young's Modulus?I_shaft - Moment of inertia of shaft?g - Acceleration due to Gravity?w - Load per unit length?L_shaft - Length of Shaft?π - Archimedes' constant?

Circular Frequency due to Uniformly Distributed Load Example

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Here is how the Circular Frequency due to Uniformly Distributed Load equation looks like with Values.

Here is how the Circular Frequency due to Uniformly Distributed Load equation looks like with Units.

Here is how the Circular Frequency due to Uniformly Distributed Load equation looks like.

5.876 = {3.1416}^{2} \cdot \sqrt{\frac{15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

5.876rad/s = {3.1416}^{2} \cdot \sqrt{\frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {3.5m}^{4}}}

5.876 = {3.1416}^{2} \cdot \sqrt{\frac{15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

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Circular Frequency due to Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Circular Frequency due to Uniformly Distributed Load?

FIRST Step Consider the formula

ω n = π^{2} \cdot \sqrt{\frac{E \cdot I shaft \cdot g}{w \cdot {L shaft}^{4}}}

Next Step Substitute values of Variables

∴

ω n = π^{2} \cdot \sqrt{\frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {3.5m}^{4}}}

Next Step Substitute values of Constants

∴

ω n = {3.1416}^{2} \cdot \sqrt{\frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {3.5m}^{4}}}

Next Step Prepare to Evaluate

∴

ω n = {3.1416}^{2} \cdot \sqrt{\frac{15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

Next Step Evaluate

∴

ω n = 5.8759895060384rad/s

LAST Step Rounding Answer

∴

ω n = 5.876rad/s

Circular Frequency due to Uniformly Distributed Load Formula Elements

Variables

Constants

Functions

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Young's Modulus

Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

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 Natural Circular Frequency

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

I shaft = \frac{5 \cdot w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load evaluator uses Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)) to evaluate the Natural Circular Frequency, Circular Frequency due to Uniformly Distributed Load formula is defined as the natural frequency of free transverse vibrations of a shaft under uniformly distributed load, which is a critical parameter in mechanical engineering to determine the shaft's vibrational behavior and stability. Natural Circular Frequency is denoted by ω_n symbol.

How to evaluate Circular Frequency due to Uniformly Distributed Load using this online evaluator? To use this online evaluator for Circular Frequency due to Uniformly Distributed Load, enter Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Circular Frequency due to Uniformly Distributed Load

What is the formula to find Circular Frequency due to Uniformly Distributed Load?

The formula of Circular Frequency due to Uniformly Distributed Load is expressed as Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). Here is an example- 5.87599 = pi^2*sqrt((15*1.085522*9.8)/(3*3.5^4)).

How to calculate Circular Frequency due to Uniformly Distributed Load?

With Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (L_shaft) we can find Circular Frequency due to Uniformly Distributed Load using the formula - Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Natural Circular Frequency?

Here are the different ways to Calculate Natural Circular Frequency-

Natural Circular Frequency=2*pi*0.5615/(sqrt(Static Deflection))

Can the Circular Frequency due to Uniformly Distributed Load be negative?

No, the Circular Frequency due to Uniformly Distributed Load, measured in Angular Velocity cannot be negative.

Which unit is used to measure Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Circular Frequency due to Uniformly Distributed Load can be measured.

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Circular Frequency due to Uniformly Distributed Load Formula

​GoCircular Frequency given Static Deflection Formula

Circular Frequency due to Uniformly Distributed Load Example

Circular Frequency due to Uniformly Distributed Load Solution

Circular Frequency due to Uniformly Distributed Load Formula Elements

Other Formulas to find Natural Circular Frequency

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Circular Frequency due to Uniformly Distributed Load?

FAQs on Circular Frequency due to Uniformly Distributed Load

Variable Name

GoCircular Frequency given Static Deflection Formula