Displacement of Body from Mean Position Calculator

✖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%
✖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%

✖Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations.ⓘ Displacement of Body from Mean Position [s_body]

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Displacement of Body from Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken)
s_body = x*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

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.
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.
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

Maximum Displacement: 1.25 Meter --> 1.25 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

s_body = x*sin(ω_n*t_total) --> 1.25*sin(21.00443027*79.9)

Evaluating ... ...

s_body = 0.750000447257092

STEP 3: Convert Result to Output's Unit

0.750000447257092 Meter --> No Conversion Required

FINAL ANSWER

0.750000447257092 ≈ 0.75 Meter <-- Displacement of Body

(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 » Mechanical » Rayleigh’s Method » Displacement of Body from Mean Position

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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

Displacement of Body from Mean Position Formula

LaTeX Go

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

Displacement of Body from Mean Position calculator uses Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken) to calculate the Displacement of Body, Displacement of Body from Mean Position formula is defined as a measure of the distance of a body from its mean position at a given time in a free longitudinal vibration, providing insight into the oscillatory motion of the body around its equilibrium position. Displacement of Body is denoted by s_body symbol.

How to calculate Displacement of Body from Mean Position using this online calculator? To use this online calculator for Displacement of Body from Mean Position, enter Maximum Displacement (x), Natural Circular Frequency (ω_n) & Total Time Taken (t_total) and hit the calculate button. Here is how the Displacement of Body from Mean Position calculation can be explained with given input values -> 0.750003 = 1.25*sin(21.00443027*79.9).

FAQ

What is Displacement of Body from Mean Position?

Displacement of Body from Mean Position formula is defined as a measure of the distance of a body from its mean position at a given time in a free longitudinal vibration, providing insight into the oscillatory motion of the body around its equilibrium position and is represented as s_body = x*sin(ω_n*t_total) or Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken). Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency, 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 Displacement of Body from Mean Position?

Displacement of Body from Mean Position formula is defined as a measure of the distance of a body from its mean position at a given time in a free longitudinal vibration, providing insight into the oscillatory motion of the body around its equilibrium position is calculated using Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken). To calculate Displacement of Body from Mean Position, you need Maximum Displacement (x), Natural Circular Frequency (ω_n) & Total Time Taken (t_total). With our tool, you need to enter the respective value for Maximum Displacement, 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.

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