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Velocity of Small Element for Transverse Vibrations Formula

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Velocity of Small Element is the speed at which a small element of a vibrating system moves in response to longitudinal and transverse vibrations. Check FAQs

v s = \frac{(3 \cdot l \cdot x^{2} - x^{3}) \cdot V traverse}{2 \cdot l^{3}}

v_s - Velocity of Small Element?l - Length of Constraint?x - Distance between Small Element and Fixed End?V_traverse - Transverse Velocity of Free End?

Velocity of Small Element for Transverse Vibrations Example

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Here is how the Velocity of Small Element for Transverse Vibrations equation looks like with Values.

Here is how the Velocity of Small Element for Transverse Vibrations equation looks like with Units.

Here is how the Velocity of Small Element for Transverse Vibrations equation looks like.

1.4865 = \frac{(3 \cdot 7.32 \cdot {3.66}^{2} - {3.66}^{3}) \cdot 4.7567}{2 \cdot {7.32}^{3}}

1.4865m/s = \frac{(3 \cdot 7.32mm \cdot {3.66mm}^{2} - {3.66mm}^{3}) \cdot 4.7567m/s}{2 \cdot {7.32mm}^{3}}

1.4865 = \frac{(3 \cdot 7.32 \cdot {3.66}^{2} - {3.66}^{3}) \cdot 4.7567}{2 \cdot {7.32}^{3}}

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Velocity of Small Element for Transverse Vibrations Solution

Follow our step by step solution on how to calculate Velocity of Small Element for Transverse Vibrations?

FIRST Step Consider the formula

v s = \frac{(3 \cdot l \cdot x^{2} - x^{3}) \cdot V traverse}{2 \cdot l^{3}}

Next Step Substitute values of Variables

∴

v s = \frac{(3 \cdot 7.32mm \cdot {3.66mm}^{2} - {3.66mm}^{3}) \cdot 4.7567m/s}{2 \cdot {7.32mm}^{3}}

Next Step Convert Units

∴

v s = \frac{(3 \cdot 0.0073m \cdot {0.0037m}^{2} - {0.0037m}^{3}) \cdot 4.7567m/s}{2 \cdot {0.0073m}^{3}}

Next Step Prepare to Evaluate

∴

v s = \frac{(3 \cdot 0.0073 \cdot {0.0037}^{2} - {0.0037}^{3}) \cdot 4.7567}{2 \cdot {0.0073}^{3}}

Next Step Evaluate

∴

v s = 1.4864709375m/s

LAST Step Rounding Answer

∴

v s = 1.4865m/s

Velocity of Small Element for Transverse Vibrations Formula Elements

Variables

Velocity of Small Element

Velocity of Small Element is the speed at which a small element of a vibrating system moves in response to longitudinal and transverse vibrations.

Symbol: v_s

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity of Small Element

Length of Constraint

Length of Constraint is the distance between the point of application of the force and the point of constraint in a vibrating system.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Constraint

Distance between Small Element and Fixed End

Distance between Small Element and Fixed End is the length between a small element and the fixed end in a vibrating system, affecting inertia constraints.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance between Small Element and Fixed End

Transverse Velocity of Free End

Transverse Velocity of Free End is the velocity of the free end of a vibrating system, influenced by the inertia of constraints in longitudinal and transverse vibrations.

Symbol: V_traverse

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Transverse Velocity of Free End

Other formulas in Transverse Vibration category

Go Total Kinetic Energy of Constraint for Transverse Vibrations

KE = \frac{33 \cdot m c \cdot {V traverse}^{2}}{280}

Go Total Mass of Constraint for Transverse Vibrations

m c = \frac{280 \cdot KE}{33 \cdot {V traverse}^{2}}

Go Transverse Velocity of Free End

V traverse = \sqrt{\frac{280 \cdot KE}{33 \cdot m c}}

Go Natural Frequency of Transverse Vibration

f = \frac{\sqrt{\frac{s constrain}{W attached + m c \cdot \frac{33}{140}}}}{2 \cdot π}

How to Evaluate Velocity of Small Element for Transverse Vibrations?

Velocity of Small Element for Transverse Vibrations evaluator uses Velocity of Small Element = ((3*Length of Constraint*Distance between Small Element and Fixed End^2-Distance between Small Element and Fixed End^3)*Transverse Velocity of Free End)/(2*Length of Constraint^3) to evaluate the Velocity of Small Element, Velocity of Small Element for Transverse Vibrations formula is defined as a measure of the velocity of a small element in a transverse vibration, which is affected by the inertia of the constraint, and is used to analyze the motion of particles in longitudinal and transverse vibrations. Velocity of Small Element is denoted by v_s symbol.

How to evaluate Velocity of Small Element for Transverse Vibrations using this online evaluator? To use this online evaluator for Velocity of Small Element for Transverse Vibrations, enter Length of Constraint (l), Distance between Small Element and Fixed End (x) & Transverse Velocity of Free End (V_traverse) and hit the calculate button.

FAQs on Velocity of Small Element for Transverse Vibrations

What is the formula to find Velocity of Small Element for Transverse Vibrations?

The formula of Velocity of Small Element for Transverse Vibrations is expressed as Velocity of Small Element = ((3*Length of Constraint*Distance between Small Element and Fixed End^2-Distance between Small Element and Fixed End^3)*Transverse Velocity of Free End)/(2*Length of Constraint^3). Here is an example- 1.486469 = ((3*0.00732*0.00366^2-0.00366^3)*4.756707)/(2*0.00732^3).

How to calculate Velocity of Small Element for Transverse Vibrations?

With Length of Constraint (l), Distance between Small Element and Fixed End (x) & Transverse Velocity of Free End (V_traverse) we can find Velocity of Small Element for Transverse Vibrations using the formula - Velocity of Small Element = ((3*Length of Constraint*Distance between Small Element and Fixed End^2-Distance between Small Element and Fixed End^3)*Transverse Velocity of Free End)/(2*Length of Constraint^3).

Can the Velocity of Small Element for Transverse Vibrations be negative?

No, the Velocity of Small Element for Transverse Vibrations, measured in Speed cannot be negative.

Which unit is used to measure Velocity of Small Element for Transverse Vibrations?

Velocity of Small Element for Transverse Vibrations is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity of Small Element for Transverse Vibrations can be measured.

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Velocity of Small Element for Transverse Vibrations Formula

Velocity of Small Element for Transverse Vibrations Example

Velocity of Small Element for Transverse Vibrations Solution

Velocity of Small Element for Transverse Vibrations Formula Elements

Other formulas in Transverse Vibration category

How to Evaluate Velocity of Small Element for Transverse Vibrations?

FAQs on Velocity of Small Element for Transverse Vibrations

Variable Name