Velocity at Mean Position 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%
✖Total Time Taken is the total time taken by the body to cover that space.ⓘ Total Time Taken [t_total]			+10% -10%

✖Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.ⓘ Velocity at Mean Position [v]

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Formula

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Velocity at Mean Position

Formula

`"v" = ("ω"_{"f"}*"x")*cos("ω"_{"f"}*"t"_{"total"})`

Example

`"54.28379m/s"=("45rad/s"*"1.25m")*cos("45rad/s"*"80s")`

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Download Rayleigh’s Method Formulas PDF

Velocity at Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)
v = (ω_f*x)*cos(ω_f*t_total)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to 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.
Total Time Taken - (Measured in Second) - Total Time Taken is the total time taken by the body to cover that space.

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
Total Time Taken: 80 Second --> 80 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = (ω_f*x)*cos(ω_f*t_total) --> (45*1.25)*cos(45*80)

Evaluating ... ...

v = 54.2837855166519

STEP 3: Convert Result to Output's Unit

54.2837855166519 Meter per Second --> No Conversion Required

FINAL ANSWER

54.2837855166519 ≈ 54.28379 Meter per Second <-- 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 » Velocity at Mean Position

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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)

Velocity at Mean Position Formula

Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)
v = (ω_f*x)*cos(ω_f*t_total)

What is a velocity?

Velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity.

How to Calculate Velocity at Mean Position?

Velocity at Mean Position calculator uses Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken) to calculate the Velocity, The Velocity at Mean Position formula is defined as the rate of change of its position with respect to a frame of reference. Velocity is denoted by v symbol.

How to calculate Velocity at Mean Position using this online calculator? To use this online calculator for Velocity at Mean Position, enter Cumulative Frequency (ω_f), Maximum Displacement (x) & Total Time Taken (t_total) and hit the calculate button. Here is how the Velocity at Mean Position calculation can be explained with given input values -> -19.169759 = (45*1.25)*cos(45*80).

FAQ

What is Velocity at Mean Position?

The Velocity at Mean Position formula is defined as the rate of change of its position with respect to a frame of reference and is represented as v = (ω_f*x)*cos(ω_f*t_total) or Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken). 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 & Total Time Taken is the total time taken by the body to cover that space.

How to calculate Velocity at Mean Position?

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