Maximum Displacement from Mean Position given Maximum Kinetic Energy Calculator

✖Maximum Kinetic Energy is the highest energy an object can attain during free longitudinal vibrations, typically observed at the natural frequency of oscillation.ⓘ Maximum Kinetic Energy [KE]			+10% -10%
✖Load is the force or weight applied to an object or structure, typically measured in kilograms, affecting its natural frequency of free longitudinal vibrations.ⓘ Load [W_load]			+10% -10%
✖Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.ⓘ Cumulative Frequency [ω_f]			+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 Kinetic Energy [x]

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Maximum Displacement from Mean Position given Maximum Kinetic Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
x = sqrt((2*KE)/(W_load*ω_f^2))
This formula uses 1 Functions, 4 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 Kinetic Energy - (Measured in Joule) - Maximum Kinetic Energy is the highest energy an object can attain during free longitudinal vibrations, typically observed at the natural frequency of oscillation.
Load - (Measured in Kilogram) - Load is the force or weight applied to an object or structure, typically measured in kilograms, affecting its natural frequency of free longitudinal vibrations.
Cumulative Frequency - (Measured in Radian per Second) - Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.

STEP 1: Convert Input(s) to Base Unit

Maximum Kinetic Energy: 7910.156 Joule --> 7910.156 Joule No Conversion Required
Load: 5 Kilogram --> 5 Kilogram No Conversion Required
Cumulative Frequency: 45 Radian per Second --> 45 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = sqrt((2*KE)/(W_load*ω_f^2)) --> sqrt((2*7910.156)/(5*45^2))

Evaluating ... ...

x = 1.24999998024691

STEP 3: Convert Result to Output's Unit

1.24999998024691 Meter --> No Conversion Required

FINAL ANSWER

1.24999998024691 ≈ 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 Kinetic Energy Formula

LaTeX Go

Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
x = sqrt((2*KE)/(W_load*ω_f^2))

What is Rayleigh's method in vibration analysis?

The 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 Kinetic Energy?

Maximum Displacement from Mean Position given Maximum Kinetic Energy calculator uses Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2)) to calculate the Maximum Displacement, Maximum Displacement from Mean Position given Maximum Kinetic Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has a certain amount of kinetic energy, which is influenced by the load and natural frequency of free longitudinal vibrations. Maximum Displacement is denoted by x symbol.

How to calculate Maximum Displacement from Mean Position given Maximum Kinetic Energy using this online calculator? To use this online calculator for Maximum Displacement from Mean Position given Maximum Kinetic Energy, enter Maximum Kinetic Energy (KE), Load (W_load) & Cumulative Frequency (ω_f) and hit the calculate button. Here is how the Maximum Displacement from Mean Position given Maximum Kinetic Energy calculation can be explained with given input values -> 1.25 = sqrt((2*7910.156)/(5*45^2)).

FAQ

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

Maximum Displacement from Mean Position given Maximum Kinetic Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has a certain amount of kinetic energy, which is influenced by the load and natural frequency of free longitudinal vibrations and is represented as x = sqrt((2*KE)/(W_load*ω_f^2)) or Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2)). Maximum Kinetic Energy is the highest energy an object can attain during free longitudinal vibrations, typically observed at the natural frequency of oscillation, Load is the force or weight applied to an object or structure, typically measured in kilograms, affecting its natural frequency of free longitudinal vibrations & Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.

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

Maximum Displacement from Mean Position given Maximum Kinetic Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has a certain amount of kinetic energy, which is influenced by the load and natural frequency of free longitudinal vibrations is calculated using Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2)). To calculate Maximum Displacement from Mean Position given Maximum Kinetic Energy, you need Maximum Kinetic Energy (KE), Load (W_load) & Cumulative Frequency (ω_f). With our tool, you need to enter the respective value for Maximum Kinetic Energy, Load & Cumulative Frequency 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 Kinetic Energy, Load & Cumulative Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
Maximum Displacement = Maximum Velocity/Natural Circular Frequency
Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

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