Maximum Displacement from Mean Position given Displacement of Body from Mean Position Calculator

✖Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations.ⓘ Displacement of Body [s_body]			+10% -10%
✖Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.ⓘ Natural Circular Frequency [ω_n]			+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 Displacement of Body from Mean Position [x]

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Maximum Displacement from Mean Position given Displacement of Body from Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))
x = s_body/(sin(ω_n*t_total))
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(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.
Displacement of Body - (Measured in Meter) - Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.
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

Displacement of Body: 0.75 Meter --> 0.75 Meter No Conversion Required
Natural Circular Frequency: 21.00443027 Radian per Second --> 21.00443027 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 = s_body/(sin(ω_n*t_total)) --> 0.75/(sin(21.00443027*79.9))

Evaluating ... ...

x = 1.24999925457196

STEP 3: Convert Result to Output's Unit

1.24999925457196 Meter --> No Conversion Required

FINAL ANSWER

1.24999925457196 ≈ 1.249999 Meter <-- Maximum Displacement

(Calculation completed in 00.004 seconds)

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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 Displacement of Body from Mean Position Formula

LaTeX Go

Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))
x = s_body/(sin(ω_n*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 Displacement of Body from Mean Position?

Maximum Displacement from Mean Position given Displacement of Body from Mean Position calculator uses Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)) to calculate the Maximum Displacement, Maximum Displacement from Mean Position given Displacement of Body from Mean Position formula is defined as the maximum distance of an object from its mean position during free longitudinal vibrations, which is a fundamental concept in physics to understand the oscillatory motion of objects. Maximum Displacement is denoted by x symbol.

How to calculate Maximum Displacement from Mean Position given Displacement of Body from Mean Position using this online calculator? To use this online calculator for Maximum Displacement from Mean Position given Displacement of Body from Mean Position, enter Displacement of Body (s_body), Natural Circular Frequency (ω_n) & Total Time Taken (t_total) and hit the calculate button. Here is how the Maximum Displacement from Mean Position given Displacement of Body from Mean Position calculation can be explained with given input values -> 1.249995 = 0.75/(sin(21.00443027*79.9)).

FAQ

What is Maximum Displacement from Mean Position given Displacement of Body from Mean Position?

Maximum Displacement from Mean Position given Displacement of Body from Mean Position formula is defined as the maximum distance of an object from its mean position during free longitudinal vibrations, which is a fundamental concept in physics to understand the oscillatory motion of objects and is represented as x = s_body/(sin(ω_n*t_total)) or Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)). Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations, Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system & 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 Displacement of Body from Mean Position?

Maximum Displacement from Mean Position given Displacement of Body from Mean Position formula is defined as the maximum distance of an object from its mean position during free longitudinal vibrations, which is a fundamental concept in physics to understand the oscillatory motion of objects is calculated using Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)). To calculate Maximum Displacement from Mean Position given Displacement of Body from Mean Position, you need Displacement of Body (s_body), Natural Circular Frequency (ω_n) & Total Time Taken (t_total). With our tool, you need to enter the respective value for Displacement of Body, Natural Circular 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 Displacement of Body, Natural Circular 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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