Acceleration of Body given Stiffness of Shaft Calculator

✖Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.ⓘ Stiffness of Shaft [s]			+10% -10%
✖Displacement of Body is defined to be the change in position of an object.ⓘ Displacement of Body [s_body]			+10% -10%
✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%

✖Acceleration is the rate of change in velocity to the change in time.ⓘ Acceleration of Body given Stiffness of Shaft [a]

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Formula

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Acceleration of Body given Stiffness of Shaft

Formula

`"a" = (-"s"*"s"_{"body"})/"W"_{"attached"}`

Example

`"-0.908654m/s²"=(-"0.63N/m"*"0.75m")/"0.52kg"`

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Download Longitudinal and Transverse Vibrations Formula PDF

Acceleration of Body given Stiffness of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint
a = (-s*s_body)/W_attached
This formula uses 4 Variables

Variables Used

Acceleration - (Measured in Meter per Square Second) - Acceleration is the rate of change in velocity to the change in time.
Stiffness of Shaft - (Measured in Newton per Meter) - Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.
Displacement of Body - (Measured in Meter) - Displacement of Body is defined to be the change in position of an object.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Shaft: 0.63 Newton per Meter --> 0.63 Newton per Meter No Conversion Required
Displacement of Body: 0.75 Meter --> 0.75 Meter No Conversion Required
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = (-s*s_body)/W_attached --> (-0.63*0.75)/0.52

Evaluating ... ...

a = -0.908653846153846

STEP 3: Convert Result to Output's Unit

-0.908653846153846 Meter per Square Second --> No Conversion Required

FINAL ANSWER

-0.908653846153846 ≈ -0.908654 Meter per Square Second <-- Acceleration

(Calculation completed in 00.005 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Acceleration of Body given Stiffness of Shaft

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National Institute Of Technology (NIT), Hamirpur

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< 8 Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft

Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Natural Frequency of Free Transverse Vibrations

Go Frequency = (sqrt(Stiffness of Shaft/Load Attached to Free End of Constraint))/2*pi

Time Period of Free Transverse Vibrations

Go Time Period = 2*pi*sqrt(Load Attached to Free End of Constraint/Stiffness of Shaft)

Acceleration of Body given Stiffness of Shaft

Go Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint

Restoring Force using Stiffness of Shaft

Go Force = -Stiffness of Shaft*Displacement of Body

Acceleration of Body given Stiffness of Shaft Formula

Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint
a = (-s*s_body)/W_attached

What is the difference between a longitudinal and transverse waves?

Transverse waves are always characterized by particle motion being perpendicular to wave motion. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves.

How to Calculate Acceleration of Body given Stiffness of Shaft?

Acceleration of Body given Stiffness of Shaft calculator uses Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint to calculate the Acceleration, The Acceleration of Body given Stiffness of Shaft formula is defined as the rate of change of the velocity of an object with respect to time. Acceleration is denoted by a symbol.

How to calculate Acceleration of Body given Stiffness of Shaft using this online calculator? To use this online calculator for Acceleration of Body given Stiffness of Shaft, enter Stiffness of Shaft (s), Displacement of Body (s_body) & Load Attached to Free End of Constraint (W_attached) and hit the calculate button. Here is how the Acceleration of Body given Stiffness of Shaft calculation can be explained with given input values -> -454.326923 = (-0.63*0.75)/0.52.

FAQ

What is Acceleration of Body given Stiffness of Shaft?

The Acceleration of Body given Stiffness of Shaft formula is defined as the rate of change of the velocity of an object with respect to time and is represented as a = (-s*s_body)/W_attached or Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint. Stiffness of shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit, Displacement of Body is defined to be the change in position of an object & Load attached to free end of constraint is a weight or source of pressure.

How to calculate Acceleration of Body given Stiffness of Shaft?

The Acceleration of Body given Stiffness of Shaft formula is defined as the rate of change of the velocity of an object with respect to time is calculated using Acceleration = (-Stiffness of Shaft*Displacement of Body)/Load Attached to Free End of Constraint. To calculate Acceleration of Body given Stiffness of Shaft, you need Stiffness of Shaft (s), Displacement of Body (s_body) & Load Attached to Free End of Constraint (W_attached). With our tool, you need to enter the respective value for Stiffness of Shaft, Displacement of Body & Load Attached to Free End of Constraint 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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