Maximum Displacement from Mean Position given Maximum Potential Energy Calculator

✖Maximum potential energy is energy that is stored or conserved in an object or substance.ⓘ Maximum Potential Energy [PE_max]			+10% -10%
✖Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%

✖Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.ⓘ Maximum Displacement from Mean Position given Maximum Potential Energy [x]

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Maximum Displacement from Mean Position given Maximum Potential Energy

Formula

`"x" = sqrt((2*"PE"_{"max"})/"s"_{"constrain"})`

Example

`"2.480695m"=sqrt((2*"40J")/"13N/m")`

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Download Rayleigh’s Method Formulas PDF

Maximum Displacement from Mean Position given Maximum Potential Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
x = sqrt((2*PE_max)/s_constrain)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Maximum Displacement - (Measured in Meter) - Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Maximum Potential Energy - (Measured in Joule) - Maximum potential energy is energy that is stored or conserved in an object or substance.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.

STEP 1: Convert Input(s) to Base Unit

Maximum Potential Energy: 40 Joule --> 40 Joule No Conversion Required
Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = sqrt((2*PE_max)/s_constrain) --> sqrt((2*40)/13)

Evaluating ... ...

x = 2.48069469178417

STEP 3: Convert Result to Output's Unit

2.48069469178417 Meter --> No Conversion Required

FINAL ANSWER

2.48069469178417 ≈ 2.480695 Meter <-- Maximum Displacement

(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 » Maximum Displacement from Mean Position given Maximum Potential Energy

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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)

Maximum Displacement from Mean Position given Maximum Potential Energy Formula

Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
x = sqrt((2*PE_max)/s_constrain)

What is Rayleigh's method in vibration analysis?

Rayleigh's quotient represents a quick method to estimate the natural frequency of a multi-degree-of-freedom vibration system, in which the mass and the stiffness matrices are known.

How to Calculate Maximum Displacement from Mean Position given Maximum Potential Energy?

Maximum Displacement from Mean Position given Maximum Potential Energy calculator uses Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint) to calculate the Maximum Displacement, The Maximum displacement from mean position given maximum potential energy formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object. Maximum Displacement is denoted by x symbol.

How to calculate Maximum Displacement from Mean Position given Maximum Potential Energy using this online calculator? To use this online calculator for Maximum Displacement from Mean Position given Maximum Potential Energy, enter Maximum Potential Energy (PE_max) & Stiffness of Constraint (s_constrain) and hit the calculate button. Here is how the Maximum Displacement from Mean Position given Maximum Potential Energy calculation can be explained with given input values -> 2.480695 = sqrt((2*40)/13).

FAQ

What is Maximum Displacement from Mean Position given Maximum Potential Energy?

The Maximum displacement from mean position given maximum potential energy formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object and is represented as x = sqrt((2*PE_max)/s_constrain) or Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint). Maximum potential energy is energy that is stored or conserved in an object or substance & Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.

How to calculate Maximum Displacement from Mean Position given Maximum Potential Energy?

The Maximum displacement from mean position given maximum potential energy formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object is calculated using Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint). To calculate Maximum Displacement from Mean Position given Maximum Potential Energy, you need Maximum Potential Energy (PE_max) & Stiffness of Constraint (s_constrain). With our tool, you need to enter the respective value for Maximum Potential Energy & Stiffness of Constraint and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum Displacement?

In this formula, Maximum Displacement uses Maximum Potential Energy & Stiffness of Constraint. We can use 4 other way(s) to calculate the same, which is/are as follows -

Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Natural Circular Frequency^2))
Maximum Displacement = Maximum Velocity/Cumulative Frequency
Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))
Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))

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