Maximum Displacement from Mean Position given Maximum Potential Energy Calculator

✖Maximum Potential Energy is the highest energy an object can store when vibrating freely at its natural frequency in a longitudinal direction.ⓘ Maximum Potential Energy [PE_max]			+10% -10%
✖Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%

✖Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency.ⓘ Maximum Displacement from Mean Position given Maximum Potential Energy [x]

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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 is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency.
Maximum Potential Energy - (Measured in Joule) - Maximum Potential Energy is the highest energy an object can store when vibrating freely at its natural frequency in a longitudinal direction.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

STEP 1: Convert Input(s) to Base Unit

Maximum Potential Energy: 10.15625 Joule --> 10.15625 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*10.15625)/13)

Evaluating ... ...

x = 1.25

STEP 3: Convert Result to Output's Unit

1.25 Meter --> No Conversion Required

FINAL ANSWER

1.25 Meter <-- Maximum Displacement

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Rayleigh’s Method Calculators

Velocity at Mean Position

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

Maximum Kinetic Energy at Mean Position

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

Maximum Potential Energy at Mean Position

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

Maximum Velocity at Mean Position by Rayleigh Method

LaTeX Go Maximum Velocity = Natural Circular Frequency*Maximum Displacement

Maximum Displacement from Mean Position given Maximum Potential Energy Formula

LaTeX Go

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, Maximum Displacement from Mean Position given Maximum Potential Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has maximum potential energy, which is useful in understanding the behavior of objects in free longitudinal vibrations. 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*10.15625)/13).

FAQ

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

Maximum Displacement from Mean Position given Maximum Potential Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has maximum potential energy, which is useful in understanding the behavior of objects in free longitudinal vibrations 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 the highest energy an object can store when vibrating freely at its natural frequency in a longitudinal direction & Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

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

Maximum Displacement from Mean Position given Maximum Potential Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has maximum potential energy, which is useful in understanding the behavior of objects in free longitudinal vibrations 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 3 other way(s) to calculate the same, which is/are as follows -

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

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