Potential Energy given Displacement of Body Calculator

✖Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%
✖Displacement of Body is defined to be the change in position of an object.ⓘ Displacement of Body [s_body]			+10% -10%

✖Potential Energy is the energy that is stored in an object due to its position relative to some zero position.ⓘ Potential Energy given Displacement of Body [PE]

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Formula

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Potential Energy given Displacement of Body

Formula

`"PE" = ("s"_{"constrain"}*("s"_{"body"}^2))/2`

Example

`"3.65625J"=("13N/m"*(("0.75m")^2))/2`

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Potential Energy given Displacement of Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2
PE = (s_constrain*(s_body^2))/2
This formula uses 3 Variables

Variables Used

Potential Energy - (Measured in Joule) - Potential Energy is the energy that is stored in an object due to its position relative to some zero position.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.
Displacement of Body - (Measured in Meter) - Displacement of Body is defined to be the change in position of an object.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
Displacement of Body: 0.75 Meter --> 0.75 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

PE = (s_constrain*(s_body^2))/2 --> (13*(0.75^2))/2

Evaluating ... ...

PE = 3.65625

STEP 3: Convert Result to Output's Unit

3.65625 Joule --> No Conversion Required

FINAL ANSWER

3.65625 Joule <-- Potential Energy

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Longitudinal Vibrations » Rayleigh’s Method » Potential Energy given Displacement of Body

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National Institute Of Technology (NIT), Hamirpur

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< 16 Rayleigh’s Method Calculators

Maximum Displacement from Mean Position given Velocity at Mean Position

Go Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

Velocity at Mean Position

Go Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)

Maximum Displacement from Mean Position given Displacement of Body from Mean Position

Go Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))

Displacement of Body from Mean Position

Go Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken)

Maximum Displacement from Mean Position given Maximum Kinetic Energy

Go Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Natural Circular Frequency^2))

Time Period of Free Longitudinal Vibrations

Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)

Natural Circular Frequency given Displacement of Body

Go Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period

Maximum Displacement from Mean Position given Maximum Potential Energy

Go Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)

Maximum Kinetic Energy at Mean Position

Go Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2

Maximum Potential Energy at Mean Position

Go Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2

Potential Energy given Displacement of Body

Go Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2

Natural Circular Frequency given Maximum Velocity at Mean Position

Go Natural Circular Frequency = Maximum Velocity/Maximum Displacement

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position

Go Maximum Displacement = Maximum Velocity/Cumulative Frequency

Maximum Velocity at Mean Position by Rayleigh Method

Go Maximum Velocity = Cumulative Frequency*Maximum Displacement

Time Period given Natural Circular Frequency

Go Time Period = (2*pi)/Natural Circular Frequency

Natural Frequency given Natural Circular Frequency

Go Frequency = Natural Circular Frequency/(2*pi)

Potential Energy given Displacement of Body Formula

Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2
PE = (s_constrain*(s_body^2))/2

What is potential energy?

Potential energy is the energy that is stored in an object due to its position relative to some zero position. An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height.

How to Calculate Potential Energy given Displacement of Body?

Potential Energy given Displacement of Body calculator uses Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2 to calculate the Potential Energy, Potential Energy given Displacement of Body is defined as the energy that is stored – or conserved - in an object or substance. Potential Energy is denoted by PE symbol.

How to calculate Potential Energy given Displacement of Body using this online calculator? To use this online calculator for Potential Energy given Displacement of Body, enter Stiffness of Constraint (s_constrain) & Displacement of Body (s_body) and hit the calculate button. Here is how the Potential Energy given Displacement of Body calculation can be explained with given input values -> 914062.5 = (13*(0.75^2))/2.

FAQ

What is Potential Energy given Displacement of Body?

Potential Energy given Displacement of Body is defined as the energy that is stored – or conserved - in an object or substance and is represented as PE = (s_constrain*(s_body^2))/2 or Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2. Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration & Displacement of Body is defined to be the change in position of an object.

How to calculate Potential Energy given Displacement of Body?

Potential Energy given Displacement of Body is defined as the energy that is stored – or conserved - in an object or substance is calculated using Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2. To calculate Potential Energy given Displacement of Body, you need Stiffness of Constraint (s_constrain) & Displacement of Body (s_body). With our tool, you need to enter the respective value for Stiffness of Constraint & Displacement of Body 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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