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Load at Free End in Free Transverse Vibrations Formula

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Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations. Check FAQs

W attached = \frac{δ \cdot 3 \cdot E \cdot I shaft}{{L shaft}^{3}}

W_attached - Load Attached to Free End of Constraint?δ - Static Deflection?E - Young's Modulus?I_shaft - Moment of inertia of shaft?L_shaft - Length of Shaft?

Load at Free End in Free Transverse Vibrations Example

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Here is how the Load at Free End in Free Transverse Vibrations equation looks like with Values.

Here is how the Load at Free End in Free Transverse Vibrations equation looks like with Units.

Here is how the Load at Free End in Free Transverse Vibrations equation looks like.

0.082 = \frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{{3.5}^{3}}

0.082kg = \frac{0.072m \cdot 3 \cdot 15N/m \cdot 1.0855kg·m²}{{3.5m}^{3}}

0.082 = \frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{{3.5}^{3}}

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Load at Free End in Free Transverse Vibrations Solution

Follow our step by step solution on how to calculate Load at Free End in Free Transverse Vibrations?

FIRST Step Consider the formula

W attached = \frac{δ \cdot 3 \cdot E \cdot I shaft}{{L shaft}^{3}}

Next Step Substitute values of Variables

∴

W attached = \frac{0.072m \cdot 3 \cdot 15N/m \cdot 1.0855kg·m²}{{3.5m}^{3}}

Next Step Prepare to Evaluate

∴

W attached = \frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{{3.5}^{3}}

Next Step Evaluate

∴

W attached = 0.0820312834985423kg

LAST Step Rounding Answer

∴

W attached = 0.082kg

Load at Free End in Free Transverse Vibrations Formula Elements

Variables

Load Attached to Free End of Constraint

Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.

Symbol: W_attached

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

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

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

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

Other formulas in General Shaft category

Go Static Deflection given Moment of Inertia of Shaft

δ = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot I shaft}

Go Length of Shaft

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{3}}

Go Moment of Inertia of Shaft given Static Deflection

I shaft = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot δ}

Go Natural Frequency of Free Transverse Vibrations

f = \frac{\sqrt{\frac{s}{W attached}}}{2} \cdot π

How to Evaluate Load at Free End in Free Transverse Vibrations?

Load at Free End in Free Transverse Vibrations evaluator uses Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3) to evaluate the Load Attached to Free End of Constraint, Load at Free End in Free Transverse Vibrations formula is defined as the maximum weight that can be attached to the free end of a shaft without causing it to vibrate excessively, which is critical in designing and optimizing mechanical systems to ensure stability and performance. Load Attached to Free End of Constraint is denoted by W_attached symbol.

How to evaluate Load at Free End in Free Transverse Vibrations using this online evaluator? To use this online evaluator for Load at Free End in Free Transverse Vibrations, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Load at Free End in Free Transverse Vibrations

What is the formula to find Load at Free End in Free Transverse Vibrations?

The formula of Load at Free End in Free Transverse Vibrations is expressed as Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3). Here is an example- 0.082031 = (0.072*3*15*1.085522)/(3.5^3).

How to calculate Load at Free End in Free Transverse Vibrations?

With Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) we can find Load at Free End in Free Transverse Vibrations using the formula - Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3).

Can the Load at Free End in Free Transverse Vibrations be negative?

No, the Load at Free End in Free Transverse Vibrations, measured in Weight cannot be negative.

Which unit is used to measure Load at Free End in Free Transverse Vibrations?

Load at Free End in Free Transverse Vibrations is usually measured using the Kilogram[kg] for Weight. Gram[kg], Milligram[kg], Ton (Metric)[kg] are the few other units in which Load at Free End in Free Transverse Vibrations can be measured.

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Load at Free End in Free Transverse Vibrations Formula

Load at Free End in Free Transverse Vibrations Example

Load at Free End in Free Transverse Vibrations Solution

Load at Free End in Free Transverse Vibrations Formula Elements

Other formulas in General Shaft category

How to Evaluate Load at Free End in Free Transverse Vibrations?

FAQs on Load at Free End in Free Transverse Vibrations

Variable Name