Velocity at Mean Position Calculator

✖Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.ⓘ Cumulative Frequency [ω_f]			+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%
✖Total Time Taken is the time required for an object to complete one free longitudinal vibration under natural frequency without any external force.ⓘ Total Time Taken [t_total]			+10% -10%

✖Velocity is the rate of change of an object's position with respect to time during free longitudinal vibrations, describing the oscillatory motion of an object.ⓘ Velocity at Mean Position [v]

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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 the rate of change of an object's position with respect to time during free longitudinal vibrations, describing the oscillatory motion of an object.
Cumulative Frequency - (Measured in Radian per Second) - Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.
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.
Total Time Taken - (Measured in Second) - Total Time Taken is the time required for an object to complete one free longitudinal vibration under natural frequency without any external force.

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: 79.9 Second --> 79.9 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*79.9)

Evaluating ... ...

v = 2.9681727213244

STEP 3: Convert Result to Output's Unit

2.9681727213244 Meter per Second --> No Conversion Required

FINAL ANSWER

2.9681727213244 ≈ 2.968173 Meter per Second <-- Velocity

(Calculation completed in 00.020 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 » Velocity at Mean Position

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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

Velocity at Mean Position Formula

LaTeX Go

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, Velocity at Mean Position formula is defined as a measure of the velocity of an object at its mean position during free longitudinal vibrations, providing insight into the object's oscillatory behavior and its natural frequency. 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 -> 2.968173 = (45*1.25)*cos(45*79.9).

FAQ

What is Velocity at Mean Position?

Velocity at Mean Position formula is defined as a measure of the velocity of an object at its mean position during free longitudinal vibrations, providing insight into the object's oscillatory behavior and its natural frequency 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). Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data, Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency & Total Time Taken is the time required for an object to complete one free longitudinal vibration under natural frequency without any external force.

How to calculate Velocity at Mean Position?

Velocity at Mean Position formula is defined as a measure of the velocity of an object at its mean position during free longitudinal vibrations, providing insight into the object's oscillatory behavior and its natural frequency 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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