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)/(ωf*cos(ωf*ttotal))
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 implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.
Cumulative Frequency - (Measured in Radian per Second) - The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
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
Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Cumulative Frequency: 45 Radian per Second --> 45 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 = (v)/(ωf*cos(ωf*ttotal)) --> (60)/(45*cos(45*80))
Evaluating ... ...
x = 1.38162803655234
STEP 3: Convert Result to Output's Unit
1.38162803655234 Meter --> No Conversion Required
FINAL ANSWER
1.38162803655234 1.381628 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 Velocity at Mean Position Formula

Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))
x = (v)/(ωf*cos(ωf*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 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, The Maximum displacement from mean position given velocity at 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 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 f) & Total Time Taken (ttotal) 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 -> -3.912412 = (60)/(45*cos(45*80)).

FAQ

What is Maximum Displacement from Mean Position given Velocity at Mean Position?
The Maximum displacement from mean position given velocity at 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 = (v)/(ωf*cos(ωf*ttotal)) or Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)). Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time, The cumulative Frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors & Total Time Taken is the total time taken by the body to cover that space.
How to calculate Maximum Displacement from Mean Position given Velocity at Mean Position?
The Maximum displacement from mean position given velocity at 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 = (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 f) & Total Time Taken (ttotal). 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 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 = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!