Maximum Potential Energy at Mean Position Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2
PEmax = (sconstrain*x^2)/2
This formula uses 3 Variables
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
Maximum Displacement: 1.25 Meter --> 1.25 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PEmax = (sconstrain*x^2)/2 --> (13*1.25^2)/2
Evaluating ... ...
PEmax = 10.15625
STEP 3: Convert Result to Output's Unit
10.15625 Joule --> No Conversion Required
FINAL ANSWER
10.15625 Joule <-- Maximum Potential Energy
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
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 Potential Energy at Mean Position Formula

Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2
PEmax = (sconstrain*x^2)/2

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 Potential Energy at Mean Position?

Maximum Potential Energy at Mean Position calculator uses Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2 to calculate the Maximum Potential Energy, The Maximum potential energy at mean position formula is defined as is energy that is stored or conserved in an object or substance. Maximum Potential Energy is denoted by PEmax symbol.

How to calculate Maximum Potential Energy at Mean Position using this online calculator? To use this online calculator for Maximum Potential Energy at Mean Position, enter Stiffness of Constraint (sconstrain) & Maximum Displacement (x) and hit the calculate button. Here is how the Maximum Potential Energy at Mean Position calculation can be explained with given input values -> 963462.5 = (13*1.25^2)/2.

FAQ

What is Maximum Potential Energy at Mean Position?
The Maximum potential energy at mean position formula is defined as is energy that is stored or conserved in an object or substance and is represented as PEmax = (sconstrain*x^2)/2 or Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2. Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration & Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
How to calculate Maximum Potential Energy at Mean Position?
The Maximum potential energy at mean position formula is defined as is energy that is stored or conserved in an object or substance is calculated using Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2. To calculate Maximum Potential Energy at Mean Position, you need Stiffness of Constraint (sconstrain) & Maximum Displacement (x). With our tool, you need to enter the respective value for Stiffness of Constraint & Maximum Displacement 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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