Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Calculator

✖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 [V_max]			+10% -10%
✖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 from Mean Position given Maximum Velocity at Mean Position [x]

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Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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 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.

STEP 1: Convert Input(s) to Base Unit

Maximum Velocity: 26.2555 Meter per Second --> 26.2555 Meter per Second No Conversion Required
Natural Circular Frequency: 21.00443027 Radian per Second --> 21.00443027 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = V_max/ω_n --> 26.2555/21.00443027

Evaluating ... ...

x = 1.24999819859432

STEP 3: Convert Result to Output's Unit

1.24999819859432 Meter --> No Conversion Required

FINAL ANSWER

1.24999819859432 ≈ 1.249998 Meter <-- Maximum Displacement

(Calculation completed in 00.007 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 Velocity at Mean Position Formula

LaTeX Go

Maximum Displacement = Maximum Velocity/Natural Circular Frequency
x = V_max/ω_n

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 Displacement from Mean Position given Maximum Velocity at Mean Position?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position calculator uses Maximum Displacement = Maximum Velocity/Natural Circular Frequency to calculate the Maximum Displacement, Maximum Displacement from Mean Position given Maximum Velocity at Mean Position formula is defined as the maximum distance an object moves from its mean position in a vibrational motion, which is a fundamental concept in the study of free longitudinal vibrations, where the object's velocity and natural frequency are crucial factors. Maximum Displacement is denoted by x symbol.

How to calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position using this online calculator? To use this online calculator for Maximum Displacement from Mean Position given Maximum Velocity at Mean Position, enter Maximum Velocity (V_max) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position calculation can be explained with given input values -> 1.249998 = 26.2555/21.00443027.

FAQ

What is Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position formula is defined as the maximum distance an object moves from its mean position in a vibrational motion, which is a fundamental concept in the study of free longitudinal vibrations, where the object's velocity and natural frequency are crucial factors and is represented as x = V_max/ω_n or Maximum Displacement = Maximum Velocity/Natural Circular Frequency. 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 is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.

How to calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position formula is defined as the maximum distance an object moves from its mean position in a vibrational motion, which is a fundamental concept in the study of free longitudinal vibrations, where the object's velocity and natural frequency are crucial factors is calculated using Maximum Displacement = Maximum Velocity/Natural Circular Frequency. To calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position, you need Maximum Velocity (V_max) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Maximum Velocity & Natural Circular 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 Velocity & Natural Circular 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 = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

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