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Static Deflection using Natural Frequency Formula

GoStatic Deflection of Simply Supported Shaft due to Uniformly Distributed Load Formula

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

δ = {(\frac{0.5615}{f})}^{2}

δ - Static Deflection?f - Frequency?

Static Deflection using Natural Frequency Example

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

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

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

3.9E-5 = {(\frac{0.5615}{90})}^{2}

3.9E-5m = {(\frac{0.5615}{90Hz})}^{2}

3.9E-5 = {(\frac{0.5615}{90})}^{2}

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Static Deflection using Natural Frequency Solution

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

FIRST Step Consider the formula

δ = {(\frac{0.5615}{f})}^{2}

Next Step Substitute values of Variables

∴

δ = {(\frac{0.5615}{90Hz})}^{2}

Next Step Prepare to Evaluate

∴

δ = {(\frac{0.5615}{90})}^{2}

Next Step Evaluate

∴

δ = 3.89237345679012E-05m

LAST Step Rounding Answer

∴

δ = 3.9E-5m

Static Deflection using Natural Frequency Formula Elements

Variables

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

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

Other Formulas to find Static Deflection

Go Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load

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

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 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}}

How to Evaluate Static Deflection using Natural Frequency?

Static Deflection using Natural Frequency evaluator uses Static Deflection = (0.5615/Frequency)^2 to evaluate the Static Deflection, Static Deflection using Natural Frequency formula is defined as a measure of the maximum displacement of an object from its equilibrium position when subjected to a force, calculated using the natural frequency of free transverse vibrations, providing insight into the object's stiffness and damping characteristics. Static Deflection is denoted by δ symbol.

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

FAQs on Static Deflection using Natural Frequency

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

The formula of Static Deflection using Natural Frequency is expressed as Static Deflection = (0.5615/Frequency)^2. Here is an example- 3.9E-5 = (0.5615/90)^2.

How to calculate Static Deflection using Natural Frequency?

With Frequency (f) we can find Static Deflection using Natural Frequency using the formula - Static Deflection = (0.5615/Frequency)^2.

What are the other ways to Calculate Static Deflection?

Here are the different ways to Calculate Static Deflection-

Static Deflection=(5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)

Can the Static Deflection using Natural Frequency be negative?

No, the Static Deflection using Natural Frequency, measured in Length cannot be negative.

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

Static Deflection using Natural Frequency is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Static Deflection using Natural Frequency can be measured.

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