FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

GoNatural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Formula

Fx Copy

LaTeX Copy

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 = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

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

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Example

With values

With units

Only example

Here is how the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) equation looks like with Values.

Here is how the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) equation looks like with Units.

Here is how the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) equation looks like.

13.3706 = \frac{2 \cdot 3.1416 \cdot 0.571}{\sqrt{0.072}}

13.3706rad/s = \frac{2 \cdot 3.1416 \cdot 0.571}{\sqrt{0.072m}}

13.3706 = \frac{2 \cdot 3.1416 \cdot 0.571}{\sqrt{0.072}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Solution

Follow our step by step solution on how to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

FIRST Step Consider the formula

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

Next Step Substitute values of Variables

∴

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{0.072m}}

Next Step Substitute values of Constants

∴

ω n = \frac{2 \cdot 3.1416 \cdot 0.571}{\sqrt{0.072m}}

Next Step Prepare to Evaluate

∴

ω n = \frac{2 \cdot 3.1416 \cdot 0.571}{\sqrt{0.072}}

Next Step Evaluate

∴

ω n = 13.3705640380808rad/s

LAST Step Rounding Answer

∴

ω n = 13.3706rad/s

Circular Frequency given Static Deflection (Shaft Fixed, 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

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 Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

ω n = \sqrt{\frac{504 \cdot E \cdot I shaft \cdot g}{w \cdot {L shaft}^{4}}}

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

δ = {(\frac{0.571}{f})}^{2}

Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

f = \frac{0.571}{\sqrt{δ}}

Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Go Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

How to Evaluate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) evaluator uses Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)) to evaluate the Natural Circular Frequency, Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the natural frequency of free transverse vibrations in a shaft under uniformly distributed load, fixed at both ends, which is essential in determining the dynamic behavior of the shaft. Natural Circular Frequency is denoted by ω_n symbol.

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

FAQs on Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

What is the formula to find Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

The formula of Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) is expressed as Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)). Here is an example- 13.37056 = (2*pi*0.571)/(sqrt(0.072)).

How to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

With Static Deflection (δ) we can find Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using the formula - Natural Circular Frequency = (2*pi*0.571)/(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=sqrt((504*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 (Shaft Fixed, Uniformly Distributed Load) be negative?

No, the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), measured in Angular Velocity cannot be negative.

Which unit is used to measure Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, 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 given Static Deflection (Shaft Fixed, Uniformly Distributed Load) can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit