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Natural Frequency given Static Deflection Formula

GoNatural Frequency due to 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{0.5615}{\sqrt{δ}}

f - Frequency?δ - Static Deflection?

Natural Frequency given Static Deflection Example

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

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

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

2.0926 = \frac{0.5615}{\sqrt{0.072}}

2.0926Hz = \frac{0.5615}{\sqrt{0.072m}}

2.0926 = \frac{0.5615}{\sqrt{0.072}}

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Natural Frequency given Static Deflection Solution

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

FIRST Step Consider the formula

f = \frac{0.5615}{\sqrt{δ}}

Next Step Substitute values of Variables

∴

f = \frac{0.5615}{\sqrt{0.072m}}

Next Step Prepare to Evaluate

∴

f = \frac{0.5615}{\sqrt{0.072}}

Next Step Evaluate

∴

f = 2.09258694894355Hz

LAST Step Rounding Answer

∴

f = 2.0926Hz

Natural Frequency given Static Deflection 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 due to Uniformly Distributed Load

f = \frac{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 Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \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 Natural Frequency given Static Deflection?

Natural Frequency given Static Deflection evaluator uses Frequency = 0.5615/(sqrt(Static Deflection)) to evaluate the Frequency, Natural Frequency given Static Deflection formula is defined as a measure of the frequency at which a system vibrates freely when displaced from its equilibrium position, providing insight into the dynamic behavior of structures and mechanical systems under various loads. Frequency is denoted by f symbol.

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

FAQs on Natural Frequency given Static Deflection

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

The formula of Natural Frequency given Static Deflection is expressed as Frequency = 0.5615/(sqrt(Static Deflection)). Here is an example- 2.092587 = 0.5615/(sqrt(0.072)).

How to calculate Natural Frequency given Static Deflection?

With Static Deflection (δ) we can find Natural Frequency given Static Deflection using the formula - Frequency = 0.5615/(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=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 Natural Frequency given Static Deflection be negative?

Yes, the Natural Frequency given Static Deflection, measured in Frequency can be negative.

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

Natural Frequency given Static Deflection 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 can be measured.

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