Velocity of Small Element for Transverse Vibrations Calculator

✖Length of Constraint is a measure of distance.ⓘ Length of Constraint [l]			+10% -10%
✖Distance between Small Element and Fixed End is a numerical measurement of how far apart objects or points are.ⓘ Distance between Small Element and Fixed End [x]			+10% -10%
✖The Transverse Velocity of Free End is the component of an object's velocity that is perpendicular to our line of sight.ⓘ Transverse Velocity of Free End [V_traverse]			+10% -10%

✖The Velocity of Small Element is the rate of change of its position with respect to a frame of reference.ⓘ Velocity of Small Element for Transverse Vibrations [v_s]

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Formula

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Velocity of Small Element for Transverse Vibrations

Formula

`"v"_{"s"} = ((3*"l"*"x"^2-"x"^3)*"V"_{"traverse"})/(2*"l"^3)`

Example

`"1.870398m/s"=((3*"7.33mm"*("3.66mm")^2-("3.66mm")^3)*"6m/s")/(2*("7.33mm")^3)`

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Download Effect of Inertia of Constraint in Longitudinal and Transverse Vibrations Formulas PDF

Velocity of Small Element for Transverse Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
v_s = ((3*l*x^2-x^3)*V_traverse)/(2*l^3)
This formula uses 4 Variables

Variables Used

Velocity of Small Element - (Measured in Meter per Second) - The Velocity of Small Element is the rate of change of its position with respect to a frame of reference.
Length of Constraint - (Measured in Meter) - Length of Constraint is a measure of distance.
Distance between Small Element and Fixed End - (Measured in Meter) - Distance between Small Element and Fixed End is a numerical measurement of how far apart objects or points are.
Transverse Velocity of Free End - (Measured in Meter per Second) - The Transverse Velocity of Free End is the component of an object's velocity that is perpendicular to our line of sight.

STEP 1: Convert Input(s) to Base Unit

Length of Constraint: 7.33 Millimeter --> 0.00733 Meter (Check conversion here)
Distance between Small Element and Fixed End: 3.66 Millimeter --> 0.00366 Meter (Check conversion here)
Transverse Velocity of Free End: 6 Meter per Second --> 6 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_s = ((3*l*x^2-x^3)*V_traverse)/(2*l^3) --> ((3*0.00733*0.00366^2-0.00366^3)*6)/(2*0.00733^3)

Evaluating ... ...

v_s = 1.87039772917666

STEP 3: Convert Result to Output's Unit

1.87039772917666 Meter per Second --> No Conversion Required

FINAL ANSWER

1.87039772917666 ≈ 1.870398 Meter per Second <-- Velocity of Small Element

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Effect of Inertia of Constraint in Longitudinal and Transverse Vibrations » Transverse Vibration » Velocity of Small Element for Transverse Vibrations

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National Institute Of Technology (NIT), Hamirpur

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< 6 Transverse Vibration Calculators

Velocity of Small Element for Transverse Vibrations

Go 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)

Natural Frequency of Transverse Vibration

Go Frequency = (sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint*33/140)))/(2*pi)

Transverse Velocity of Free End

Go Transverse Velocity of Free End = sqrt((280*Kinetic Energy)/(33*Total Mass of Constraint))

Total Mass of Constraint for Transverse Vibrations

Go Total Mass of Constraint = (280*Kinetic Energy)/(33*Transverse Velocity of Free End^2)

Total Kinetic Energy of Constraint for Transverse Vibrations

Go Kinetic Energy = (33*Total Mass of Constraint*Transverse Velocity of Free End^2)/280

Length of Constraint for Transverse Vibrations

Go Length of Constraint = Total Mass of Constraint/Mass

Velocity of Small Element for Transverse Vibrations Formula

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Velocity of Small Element for Transverse Vibrations?

Velocity of Small Element for Transverse Vibrations calculator 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 calculate the Velocity of Small Element, The Velocity of small element for transverse vibrations formula is defined as the rate of change of its position with respect to a frame of reference. Velocity of Small Element is denoted by v_s symbol.

How to calculate Velocity of Small Element for Transverse Vibrations using this online calculator? To use this online calculator 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. Here is how the Velocity of Small Element for Transverse Vibrations calculation can be explained with given input values -> 0.467017 = ((3*0.00733*0.00366^2-0.00366^3)*6)/(2*0.00733^3).

FAQ

What is Velocity of Small Element for Transverse Vibrations?

The Velocity of small element for transverse vibrations formula is defined as the rate of change of its position with respect to a frame of reference and is represented as v_s = ((3*l*x^2-x^3)*V_traverse)/(2*l^3) or 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). Length of Constraint is a measure of distance, Distance between Small Element and Fixed End is a numerical measurement of how far apart objects or points are & The Transverse Velocity of Free End is the component of an object's velocity that is perpendicular to our line of sight.

How to calculate Velocity of Small Element for Transverse Vibrations?

The Velocity of small element for transverse vibrations formula is defined as the rate of change of its position with respect to a frame of reference is calculated using 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 calculate Velocity of Small Element for Transverse Vibrations, you need Length of Constraint (l), Distance between Small Element and Fixed End (x) & Transverse Velocity of Free End (V_traverse). With our tool, you need to enter the respective value for Length of Constraint, Distance between Small Element and Fixed End & Transverse Velocity of Free End and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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