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Circular Frequency given Static Deflection Formula

GoCircular Frequency due to Uniformly Distributed Load 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 = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

ω_n - Natural Circular Frequency?δ - Static Deflection?π - Archimedes' constant?

Circular Frequency given Static Deflection Example

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Here is how the Circular Frequency given Static Deflection equation looks like with Values.

Here is how the Circular Frequency given Static Deflection equation looks like with Units.

Here is how the Circular Frequency given Static Deflection equation looks like.

13.1481 = 2 \cdot 3.1416 \cdot \frac{0.5615}{\sqrt{0.072}}

13.1481rad/s = 2 \cdot 3.1416 \cdot \frac{0.5615}{\sqrt{0.072m}}

13.1481 = 2 \cdot 3.1416 \cdot \frac{0.5615}{\sqrt{0.072}}

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Circular Frequency given Static Deflection Solution

Follow our step by step solution on how to calculate Circular Frequency given Static Deflection?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{0.072m}}

Next Step Substitute values of Constants

∴

ω n = 2 \cdot 3.1416 \cdot \frac{0.5615}{\sqrt{0.072m}}

Next Step Prepare to Evaluate

∴

ω n = 2 \cdot 3.1416 \cdot \frac{0.5615}{\sqrt{0.072}}

Next Step Evaluate

∴

ω n = 13.1481115715979rad/s

LAST Step Rounding Answer

∴

ω n = 13.1481rad/s

Circular Frequency given Static Deflection 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

Static Deflection

Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

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 Natural Circular Frequency

Go Circular Frequency due to Uniformly Distributed Load

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

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 given Static Deflection?

Circular Frequency given Static Deflection evaluator uses Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection)) to evaluate the Natural Circular Frequency, Circular Frequency given Static Deflection formula is defined as a measure of the natural frequency of free transverse vibrations in a system, providing insight into the oscillatory behavior of a structure under external forces, with applications in mechanical and civil engineering. Natural Circular Frequency is denoted by ω_n symbol.

How to evaluate Circular Frequency given Static Deflection using this online evaluator? To use this online evaluator for Circular Frequency given Static Deflection, enter Static Deflection (δ) and hit the calculate button.

FAQs on Circular Frequency given Static Deflection

What is the formula to find Circular Frequency given Static Deflection?

The formula of Circular Frequency given Static Deflection is expressed as Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection)). Here is an example- 13.14811 = 2*pi*0.5615/(sqrt(0.072)).

How to calculate Circular Frequency given Static Deflection?

With Static Deflection (δ) we can find Circular Frequency given Static Deflection using the formula - Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection)). 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=pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Can the Circular Frequency given Static Deflection be negative?

No, the Circular Frequency given Static Deflection, measured in Angular Velocity cannot be negative.

Which unit is used to measure Circular Frequency given Static Deflection?

Circular Frequency given Static Deflection 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 given Static Deflection can be measured.

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