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 = sbody/(sin(ωn*ttotal))
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 implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Displacement of Body - (Measured in Meter) - Displacement of Body 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
Displacement of Body: 0.75 Meter --> 0.75 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
x = sbody/(sin(ωn*ttotal)) --> 0.75/(sin(21*80))
Evaluating ... ...
x = 1.0978528642788
STEP 3: Convert Result to Output's Unit
1.0978528642788 Meter --> No Conversion Required
FINAL ANSWER
1.0978528642788 1.097853 Meter <-- Maximum Displacement
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

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)

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

Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))
x = sbody/(sin(ωn*ttotal))

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, The Maximum displacement from mean position given 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. 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 (sbody), Natural Circular Frequency n) & Total Time Taken (ttotal) 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 -> 1.097853 = 0.75/(sin(21*80)).

FAQ

What is Maximum Displacement from Mean Position given Displacement of Body from Mean Position?
The Maximum displacement from mean position given 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 x = sbody/(sin(ωn*ttotal)) or Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)). Displacement of Body 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 Maximum Displacement from Mean Position given Displacement of Body from Mean Position?
The Maximum displacement from mean position given 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 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 (sbody), Natural Circular Frequency n) & Total Time Taken (ttotal). 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 4 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*Natural Circular Frequency^2))
  • Maximum Displacement = Maximum Velocity/Cumulative Frequency
  • Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!