Displacement of Body from Mean Position Calculator

✖Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.ⓘ Maximum Displacement [x]			+10% -10%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖Total Time Taken is the total time taken by the body to cover that space.ⓘ Total Time Taken [t_total]			+10% -10%

✖Displacement of Body is defined to be the change in position of an object.ⓘ Displacement of Body from Mean Position [s_body]

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Formula

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Displacement of Body from Mean Position

Formula

`"s"_{"body"} = "x"*sin("ω"_{"n"}*"t"_{"total"})`

Example

`"0.85394m"="1.25m"*sin("21rad/s"*"80s")`

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Download Rayleigh’s Method Formulas PDF

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 defined to be the change in position of an object.
Maximum Displacement - (Measured in Meter) - Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Total Time Taken - (Measured in Second) - Total Time Taken is the total time taken by the body to cover that space.

STEP 1: Convert Input(s) to Base Unit

Maximum Displacement: 1.25 Meter --> 1.25 Meter No Conversion Required
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Total Time Taken: 80 Second --> 80 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*80)

Evaluating ... ...

s_body = 0.853939567408117

STEP 3: Convert Result to Output's Unit

0.853939567408117 Meter --> No Conversion Required

FINAL ANSWER

0.853939567408117 ≈ 0.85394 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 » Rayleigh’s Method » Displacement of Body from Mean Position

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National Institute Of Technology (NIT), Hamirpur

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< 16 Rayleigh’s Method Calculators

Maximum Displacement from Mean Position given Velocity at Mean Position

Go Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

Velocity at Mean Position

Go Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)

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

Go Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))

Displacement of Body from Mean Position

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

Maximum Displacement from Mean Position given Maximum Kinetic Energy

Go Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Natural Circular Frequency^2))

Time Period of Free Longitudinal Vibrations

Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)

Natural Circular Frequency given Displacement of Body

Go Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period

Maximum Displacement from Mean Position given Maximum Potential Energy

Go Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)

Maximum Kinetic Energy at Mean Position

Go Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2

Maximum Potential Energy at Mean Position

Go Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2

Potential Energy given Displacement of Body

Go Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2

Natural Circular Frequency given Maximum Velocity at Mean Position

Go Natural Circular Frequency = Maximum Velocity/Maximum Displacement

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position

Go Maximum Displacement = Maximum Velocity/Cumulative Frequency

Maximum Velocity at Mean Position by Rayleigh Method

Go Maximum Velocity = Cumulative Frequency*Maximum Displacement

Time Period given Natural Circular Frequency

Go Time Period = (2*pi)/Natural Circular Frequency

Natural Frequency given Natural Circular Frequency

Go Frequency = Natural Circular Frequency/(2*pi)

Displacement of Body from Mean Position Formula

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, The Displacement of body from mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object. 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 -> 263.0134 = 1.25*sin(21*80).

FAQ

What is Displacement of Body from Mean Position?

The Displacement of body from mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object 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 implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object, Natural Circular Frequency is a scalar measure of rotation rate & Total Time Taken is the total time taken by the body to cover that space.

How to calculate Displacement of Body from Mean Position?

The Displacement of body from mean position formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in the position of an object 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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