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Uniformly Distributed Load Unit Length given Natural Frequency Formula

GoUniformly Distributed Load Unit Length given Static Deflection Formula

GoUniformly Distributed Load Unit Length given Circular Frequency Formula

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Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations. Check FAQs

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

w - Load per unit length?f - Frequency?E - Young's Modulus?I_shaft - Moment of inertia of shaft?g - Acceleration due to Gravity?L_shaft - Length of Shaft?π - Archimedes' constant?

Uniformly Distributed Load Unit Length given Natural Frequency Example

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Here is how the Uniformly Distributed Load Unit Length given Natural Frequency equation looks like with Values.

Here is how the Uniformly Distributed Load Unit Length given Natural Frequency equation looks like with Units.

Here is how the Uniformly Distributed Load Unit Length given Natural Frequency equation looks like.

0.0003 = \frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4}}

0.0003 = \frac{{3.1416}^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4}}

0.0003 = \frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4}}

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Uniformly Distributed Load Unit Length given Natural Frequency Solution

Follow our step by step solution on how to calculate Uniformly Distributed Load Unit Length given Natural Frequency?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w = \frac{π^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4}}

Next Step Substitute values of Constants

∴

w = \frac{{3.1416}^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{{3.5m}^{4}}

Next Step Prepare to Evaluate

∴

w = \frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{{3.5}^{4}}

Next Step Evaluate

∴

w = 0.000323920565644122

LAST Step Rounding Answer

∴

w = 0.0003

Uniformly Distributed Load Unit Length given Natural Frequency Formula Elements

Variables

Constants

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

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

Young's Modulus

Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

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

Other Formulas to find Load per unit length

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 Uniformly Distributed Load Unit Length given Circular Frequency

w = \frac{π^{4}}{{ω n}^{2}} \cdot \frac{E \cdot I shaft \cdot g}{{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 Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

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 Uniformly Distributed Load Unit Length given Natural Frequency?

Uniformly Distributed Load Unit Length given Natural Frequency evaluator uses Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4) to evaluate the Load per unit length, Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as a measure of the load per unit length of a shaft in a mechanical system, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the shaft's modulus of elasticity, moment of inertia, and length. Load per unit length is denoted by w symbol.

How to evaluate Uniformly Distributed Load Unit Length given Natural Frequency using this online evaluator? To use this online evaluator for Uniformly Distributed Load Unit Length given Natural Frequency, enter Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Uniformly Distributed Load Unit Length given Natural Frequency

What is the formula to find Uniformly Distributed Load Unit Length given Natural Frequency?

The formula of Uniformly Distributed Load Unit Length given Natural Frequency is expressed as Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4). Here is an example- 0.000324 = (pi^2)/(4*90^2)*(15*1.085522*9.8)/(3.5^4).

How to calculate Uniformly Distributed Load Unit Length given Natural Frequency?

With Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Length of Shaft (L_shaft) we can find Uniformly Distributed Load Unit Length given Natural Frequency using the formula - Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4). This formula also uses Archimedes' constant .

What are the other ways to Calculate Load per unit length?

Here are the different ways to Calculate Load per unit length-

Load per unit length=(Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)
Load per unit length=(pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

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Uniformly Distributed Load Unit Length given Natural Frequency Formula

​GoUniformly Distributed Load Unit Length given Static Deflection Formula

​GoUniformly Distributed Load Unit Length given Circular Frequency Formula

Uniformly Distributed Load Unit Length given Natural Frequency Example

Uniformly Distributed Load Unit Length given Natural Frequency Solution

Uniformly Distributed Load Unit Length given Natural Frequency Formula Elements

Other Formulas to find Load per unit length

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Uniformly Distributed Load Unit Length given Natural Frequency?

FAQs on Uniformly Distributed Load Unit Length given Natural Frequency

Variable Name

GoUniformly Distributed Load Unit Length given Static Deflection Formula

GoUniformly Distributed Load Unit Length given Circular Frequency Formula