Maximum Velocity at Mean Position by Rayleigh Method Calculator

✖Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.ⓘ Natural Circular Frequency [ω_n]			+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 Velocity is the highest speed achieved by an object undergoing free longitudinal vibrations, typically occurring at the natural frequency of the system.ⓘ Maximum Velocity at Mean Position by Rayleigh Method [V_max]

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Maximum Velocity at Mean Position by Rayleigh Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Velocity = Natural Circular Frequency*Maximum Displacement
V_max = ω_n*x
This formula uses 3 Variables

Variables Used

Maximum Velocity - (Measured in Meter per Second) - Maximum Velocity is the highest speed achieved by an object undergoing free longitudinal vibrations, typically occurring at the natural frequency of the system.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.
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

Natural Circular Frequency: 21.00443027 Radian per Second --> 21.00443027 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_n*x --> 21.00443027*1.25

Evaluating ... ...

V_max = 26.2555378375

STEP 3: Convert Result to Output's Unit

26.2555378375 Meter per Second --> No Conversion Required

FINAL ANSWER

26.2555378375 ≈ 26.25554 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 » Mechanical » 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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< 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 Velocity at Mean Position by Rayleigh Method Formula

LaTeX Go

Maximum Velocity = Natural Circular Frequency*Maximum Displacement
V_max = ω_n*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 = Natural Circular Frequency*Maximum Displacement to calculate the Maximum Velocity, Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the highest velocity attained by an object at its mean position during free longitudinal vibrations, providing valuable insights into the oscillatory motion of the object. 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 Natural Circular Frequency (ω_n) & 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 -> 26.25554 = 21.00443027*1.25.

FAQ

What is Maximum Velocity at Mean Position by Rayleigh Method?

Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the highest velocity attained by an object at its mean position during free longitudinal vibrations, providing valuable insights into the oscillatory motion of the object and is represented as V_max = ω_n*x or Maximum Velocity = Natural Circular Frequency*Maximum Displacement. Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system & 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 Velocity at Mean Position by Rayleigh Method?

Maximum Velocity at Mean Position by Rayleigh Method formula is defined as the highest velocity attained by an object at its mean position during free longitudinal vibrations, providing valuable insights into the oscillatory motion of the object is calculated using Maximum Velocity = Natural Circular Frequency*Maximum Displacement. To calculate Maximum Velocity at Mean Position by Rayleigh Method, you need Natural Circular Frequency (ω_n) & Maximum Displacement (x). With our tool, you need to enter the respective value for Natural Circular 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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