Maximum Kinetic Energy at Mean Position Calculator

✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load [W_load]			+10% -10%
✖The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.ⓘ Cumulative Frequency [ω_f]			+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 [x]			+10% -10%

✖Maximum kinetic energy is the energy that it possesses due to its motion.ⓘ Maximum Kinetic Energy at Mean Position [KE]

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Maximum Kinetic Energy at Mean Position

Formula

`"KE" = ("W"_{"load"}*"ω"_{"f"}^2*"x"^2)/2`

Example

`"7910.156J"=("5kg"*("45rad/s")^2*("1.25m")^2)/2`

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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 energy that it possesses due to its motion.
Load - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Cumulative Frequency - (Measured in Radian per Second) - The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
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

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 » Rayleigh’s Method » Maximum Kinetic Energy at Mean Position

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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 Kinetic Energy at Mean Position Formula

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, The Maximum kinetic energy at mean position formula is defined as is the energy that it possesses due to its motion. 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 -> 1722.656 = (5*45^2*1.25^2)/2.

FAQ

What is Maximum Kinetic Energy at Mean Position?

The Maximum kinetic energy at mean position formula is defined as is the energy that it possesses due to its motion 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 attached to free end of constraint is a weight or source of pressure, The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors & 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 Kinetic Energy at Mean Position?

The Maximum kinetic energy at mean position formula is defined as is the energy that it possesses due to its motion 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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