Natural Frequency given Natural Circular Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = Natural Circular Frequency/(2*pi)
f = ωn/(2*pi)
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
STEP 1: Convert Input(s) to Base Unit
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = ωn/(2*pi) --> 21/(2*pi)
Evaluating ... ...
f = 3.3422538049298
STEP 3: Convert Result to Output's Unit
3.3422538049298 Hertz --> No Conversion Required
FINAL ANSWER
3.3422538049298 3.342254 Hertz <-- Frequency
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Birsa Institute of Technology (BIT), Sindri
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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)

Natural Frequency given Natural Circular Frequency Formula

Frequency = Natural Circular Frequency/(2*pi)
f = ωn/(2*pi)

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 Natural Frequency given Natural Circular Frequency?

Natural Frequency given Natural Circular Frequency calculator uses Frequency = Natural Circular Frequency/(2*pi) to calculate the Frequency, The Natural Frequency given Natural Circular Frequency formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force. Frequency is denoted by f symbol.

How to calculate Natural Frequency given Natural Circular Frequency using this online calculator? To use this online calculator for Natural Frequency given Natural Circular Frequency, enter Natural Circular Frequency n) and hit the calculate button. Here is how the Natural Frequency given Natural Circular Frequency calculation can be explained with given input values -> 3.342254 = 21/(2*pi).

FAQ

What is Natural Frequency given Natural Circular Frequency?
The Natural Frequency given Natural Circular Frequency formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force and is represented as f = ωn/(2*pi) or Frequency = Natural Circular Frequency/(2*pi). Natural Circular Frequency is a scalar measure of rotation rate.
How to calculate Natural Frequency given Natural Circular Frequency?
The Natural Frequency given Natural Circular Frequency formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force is calculated using Frequency = Natural Circular Frequency/(2*pi). To calculate Natural Frequency given Natural Circular Frequency, you need Natural Circular Frequency n). With our tool, you need to enter the respective value for Natural Circular Frequency 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 Frequency?
In this formula, Frequency uses Natural Circular Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period
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