Maximum Displacement from Mean Position given Velocity at Mean Position Calculator

✖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 [v]			+10% -10%
✖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%
✖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%

✖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 Velocity at Mean Position [x]

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Maximum Displacement from Mean Position given Velocity at Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Velocity: 2.968173 Meter per Second --> 2.968173 Meter per Second No Conversion Required
Cumulative Frequency: 45 Radian per Second --> 45 Radian per Second No Conversion Required
Total Time Taken: 79.9 Second --> 79.9 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = (v)/(ω_f*cos(ω_f*t_total)) --> (2.968173)/(45*cos(45*79.9))

Evaluating ... ...

x = 1.25000011735992

STEP 3: Convert Result to Output's Unit

1.25000011735992 Meter --> No Conversion Required

FINAL ANSWER

1.25000011735992 ≈ 1.25 Meter <-- Maximum Displacement

(Calculation completed in 00.020 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 Velocity at Mean Position Formula

LaTeX Go

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

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 Velocity at Mean Position?

Maximum Displacement from Mean Position given Velocity at Mean Position calculator uses Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)) to calculate the Maximum Displacement, Maximum Displacement from Mean Position given Velocity at Mean Position formula is defined as the maximum distance of an object from its mean position in a vibrational motion, which is a critical parameter in understanding the dynamics of free longitudinal vibrations, particularly in the context of natural frequency. Maximum Displacement is denoted by x symbol.

How to calculate Maximum Displacement from Mean Position given Velocity at Mean Position using this online calculator? To use this online calculator for Maximum Displacement from Mean Position given Velocity at Mean Position, enter Velocity (v), Cumulative Frequency (ω_f) & Total Time Taken (t_total) and hit the calculate button. Here is how the Maximum Displacement from Mean Position given Velocity at Mean Position calculation can be explained with given input values -> 25.26807 = (2.968173)/(45*cos(45*79.9)).

FAQ

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

Maximum Displacement from Mean Position given Velocity at Mean Position formula is defined as the maximum distance of an object from its mean position in a vibrational motion, which is a critical parameter in understanding the dynamics of free longitudinal vibrations, particularly in the context of natural frequency and is represented as x = (v)/(ω_f*cos(ω_f*t_total)) or Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)). 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 is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data & 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 Maximum Displacement from Mean Position given Velocity at Mean Position?

Maximum Displacement from Mean Position given Velocity at Mean Position formula is defined as the maximum distance of an object from its mean position in a vibrational motion, which is a critical parameter in understanding the dynamics of free longitudinal vibrations, particularly in the context of natural frequency is calculated using Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)). To calculate Maximum Displacement from Mean Position given Velocity at Mean Position, you need Velocity (v), Cumulative Frequency (ω_f) & Total Time Taken (t_total). With our tool, you need to enter the respective value for Velocity, Cumulative Frequency & Total Time Taken 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 Velocity, Cumulative Frequency & Total Time Taken. 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 = Maximum Velocity/Natural Circular Frequency

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