Maximum Velocity at Mean Position by Rayleigh Method Calculator

✖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 Velocity is the rate of change of its position with respect to a frame of reference, and is a function of time.ⓘ Maximum Velocity at Mean Position by Rayleigh Method [V_max]

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Formula

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Maximum Velocity at Mean Position by Rayleigh Method

Formula

`"V"_{"max"} = "ω"_{"f"}*"x"`

Example

`"56.25m/s"="45rad/s"*"1.25m"`

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Download Rayleigh’s Method Formulas PDF

Maximum Velocity at Mean Position by Rayleigh Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Velocity = Cumulative Frequency*Maximum Displacement
V_max = ω_f*x
This formula uses 3 Variables

Variables Used

Maximum Velocity - (Measured in Meter per Second) - Maximum Velocity is the rate of change of its position with respect to a frame of reference, and is a function of time.
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

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

V_max = ω_f*x --> 45*1.25

Evaluating ... ...

V_max = 56.25

STEP 3: Convert Result to Output's Unit

56.25 Meter per Second --> No Conversion Required

FINAL ANSWER

56.25 Meter per Second <-- Maximum Velocity

(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 Velocity at Mean Position by Rayleigh Method

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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 Velocity at Mean Position by Rayleigh Method Formula

Maximum Velocity = Cumulative Frequency*Maximum Displacement
V_max = ω_f*x

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 Velocity at Mean Position by Rayleigh Method?

Maximum Velocity at Mean Position by Rayleigh Method calculator uses Maximum Velocity = Cumulative Frequency*Maximum Displacement to calculate the Maximum Velocity, The Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the rate of change of its position with respect to a frame of reference. Maximum Velocity is denoted by V_max symbol.

How to calculate Maximum Velocity at Mean Position by Rayleigh Method using this online calculator? To use this online calculator for Maximum Velocity at Mean Position by Rayleigh Method, enter Cumulative Frequency (ω_f) & Maximum Displacement (x) and hit the calculate button. Here is how the Maximum Velocity at Mean Position by Rayleigh Method calculation can be explained with given input values -> 26.25 = 45*1.25.

FAQ

What is Maximum Velocity at Mean Position by Rayleigh Method?

The Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the rate of change of its position with respect to a frame of reference and is represented as V_max = ω_f*x or Maximum Velocity = Cumulative Frequency*Maximum Displacement. 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 Velocity at Mean Position by Rayleigh Method?

The Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the rate of change of its position with respect to a frame of reference is calculated using Maximum Velocity = Cumulative Frequency*Maximum Displacement. To calculate Maximum Velocity at Mean Position by Rayleigh Method, you need Cumulative Frequency (ω_f) & Maximum Displacement (x). With our tool, you need to enter the respective value for 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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