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

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

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Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior. Check FAQs

f = \frac{0.571}{\sqrt{δ}}

f - Frequency?δ - Static Deflection?

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

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

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

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

2.128 = \frac{0.571}{\sqrt{0.072}}

2.128Hz = \frac{0.571}{\sqrt{0.072m}}

2.128 = \frac{0.571}{\sqrt{0.072}}

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

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

FIRST Step Consider the formula

f = \frac{0.571}{\sqrt{δ}}

Next Step Substitute values of Variables

∴

f = \frac{0.571}{\sqrt{0.072m}}

Next Step Prepare to Evaluate

∴

f = \frac{0.571}{\sqrt{0.072}}

Next Step Evaluate

∴

f = 2.1279913585873Hz

LAST Step Rounding Answer

∴

f = 2.128Hz

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

Variables

Functions

Frequency

Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find 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

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 Frequency

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

f = 3.573 \cdot \sqrt{\frac{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 Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

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

δ = {(\frac{0.571}{f})}^{2}

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

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) evaluator uses Frequency = 0.571/(sqrt(Static Deflection)) to evaluate the Frequency, Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the frequency at which a shaft with a fixed end and uniformly distributed load vibrates freely in a transverse direction, providing insight into the shaft's natural frequency of vibration. Frequency is denoted by f symbol.

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

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

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

The formula of Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) is expressed as Frequency = 0.571/(sqrt(Static Deflection)). Here is an example- 2.127991 = 0.571/(sqrt(0.072)).

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

With Static Deflection (δ) we can find Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using the formula - Frequency = 0.571/(sqrt(Static Deflection)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Frequency?

Here are the different ways to Calculate Frequency-

Frequency=3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Can the Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) be negative?

Yes, the Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), measured in Frequency can be negative.

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

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) can be measured.

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