Maximum Kinetic Energy at Mean Position Calculator

✖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 [x]			+10% -10%

✖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 at Mean Position [KE]

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Maximum Kinetic Energy at Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2
KE = (W_load*ω_f^2*x^2)/2
This formula uses 4 Variables

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Load: 5 Kilogram --> 5 Kilogram No Conversion Required
Cumulative Frequency: 45 Radian per Second --> 45 Radian per Second No Conversion Required
Maximum Displacement: 1.25 Meter --> 1.25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

KE = (W_load*ω_f^2*x^2)/2 --> (5*45^2*1.25^2)/2

Evaluating ... ...

KE = 7910.15625

STEP 3: Convert Result to Output's Unit

7910.15625 Joule --> No Conversion Required

FINAL ANSWER

7910.15625 ≈ 7910.156 Joule <-- Maximum Kinetic 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 » Mechanical » Rayleigh’s Method » Maximum Kinetic Energy at Mean Position

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National Institute Of Technology (NIT), Hamirpur

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< Rayleigh’s Method Calculators

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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 Kinetic Energy at Mean Position Formula

LaTeX Go

Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2
KE = (W_load*ω_f^2*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 Kinetic Energy at Mean Position?

Maximum Kinetic Energy at Mean Position calculator uses Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2 to calculate the Maximum Kinetic Energy, Maximum Kinetic Energy at Mean Position formula is defined as the maximum energy an object possesses due to its motion at a mean position, which is a crucial concept in understanding the dynamics of free longitudinal vibrations, particularly in mechanical systems. Maximum Kinetic Energy is denoted by KE symbol.

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

FAQ

What is Maximum Kinetic Energy at Mean Position?

Maximum Kinetic Energy at Mean Position formula is defined as the maximum energy an object possesses due to its motion at a mean position, which is a crucial concept in understanding the dynamics of free longitudinal vibrations, particularly in mechanical systems and is represented as KE = (W_load*ω_f^2*x^2)/2 or Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2. 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 & Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency.

How to calculate Maximum Kinetic Energy at Mean Position?

Maximum Kinetic Energy at Mean Position formula is defined as the maximum energy an object possesses due to its motion at a mean position, which is a crucial concept in understanding the dynamics of free longitudinal vibrations, particularly in mechanical systems is calculated using Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2. To calculate Maximum Kinetic Energy at Mean Position, you need Load (W_load), Cumulative Frequency (ω_f) & Maximum Displacement (x). With our tool, you need to enter the respective value for Load, Cumulative Frequency & 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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