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

✖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 [V_max]			+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 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

Formula

`"x" = "V"_{"max"}/"ω"_{"f"}`

Example

`"1.666667m"="75m/s"/"45rad/s"`

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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/Cumulative Frequency
x = V_max/ω_f
This formula uses 3 Variables

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Maximum Velocity: 75 Meter per Second --> 75 Meter per Second No Conversion Required
Cumulative Frequency: 45 Radian per Second --> 45 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = V_max/ω_f --> 75/45

Evaluating ... ...

x = 1.66666666666667

STEP 3: Convert Result to Output's Unit

1.66666666666667 Meter --> No Conversion Required

FINAL ANSWER

1.66666666666667 ≈ 1.666667 Meter <-- Maximum Displacement

(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 Displacement from Mean Position given Maximum Velocity at Mean Position

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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 Displacement from Mean Position given Maximum Velocity at Mean Position Formula

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

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/Cumulative Frequency to calculate the Maximum Displacement, The Maximum displacement from mean position given maximum velocity at mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object. 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) & Cumulative Frequency (ω_f) 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 -> 3.571429 = 75/45.

FAQ

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

The Maximum displacement from mean position given maximum velocity at mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object and is represented as x = V_max/ω_f or Maximum Displacement = Maximum Velocity/Cumulative Frequency. Maximum Velocity is the rate of change of its position with respect to a frame of reference, and is a function of time & The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

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

The Maximum displacement from mean position given maximum velocity at mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object is calculated using Maximum Displacement = Maximum Velocity/Cumulative Frequency. To calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position, you need Maximum Velocity (V_max) & Cumulative Frequency (ω_f). With our tool, you need to enter the respective value for Maximum Velocity & Cumulative 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 & Cumulative Frequency. We can use 4 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*Natural Circular Frequency^2))
Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))
Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))

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