Velocity at Mean Position Solution

STEP 0: Pre-Calculation Summary
Formula Used
Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)
v = (ωf*x)*cos(ωf*ttotal)
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 = (ωf*x)*cos(ωf*ttotal) --> (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 00.004 seconds)

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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 = (ωf*x)*cos(ωf*ttotal)

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 f), Maximum Displacement (x) & Total Time Taken (ttotal) 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 = (ωf*x)*cos(ωf*ttotal) 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 f), Maximum Displacement (x) & Total Time Taken (ttotal). 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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