Natural Circular Frequency given Displacement of Body Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period
f = (asin(sbody/x))/tp
This formula uses 2 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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)
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.
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.
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
STEP 1: Convert Input(s) to Base Unit
Displacement of Body: 0.75 Meter --> 0.75 Meter No Conversion Required
Maximum Displacement: 1.25 Meter --> 1.25 Meter No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = (asin(sbody/x))/tp --> (asin(0.75/1.25))/3
Evaluating ... ...
f = 0.214500369597761
STEP 3: Convert Result to Output's Unit
0.214500369597761 Hertz --> No Conversion Required
FINAL ANSWER
0.214500369597761 0.2145 Hertz <-- Frequency
(Calculation completed in 00.004 seconds)

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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)

Natural Circular Frequency given Displacement of Body Formula

Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period
f = (asin(sbody/x))/tp

What is Rayleigh's method in vibration analysis?

The 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 Circular Frequency given Displacement of Body?

Natural Circular Frequency given Displacement of Body calculator uses Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period to calculate the Frequency, The Natural Circular Frequency given Displacement of Body formula is defined as a scalar measure of rotation rate. Frequency is denoted by f symbol.

How to calculate Natural Circular Frequency given Displacement of Body using this online calculator? To use this online calculator for Natural Circular Frequency given Displacement of Body, enter Displacement of Body (sbody), Maximum Displacement (x) & Time Period (tp) and hit the calculate button. Here is how the Natural Circular Frequency given Displacement of Body calculation can be explained with given input values -> 0.2145 = (asin(0.75/1.25))/3.

FAQ

What is Natural Circular Frequency given Displacement of Body?
The Natural Circular Frequency given Displacement of Body formula is defined as a scalar measure of rotation rate and is represented as f = (asin(sbody/x))/tp or Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period. Displacement of Body is defined to be the change in position of an object, Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object & Time Period is the time taken by a complete cycle of the wave to pass a point.
How to calculate Natural Circular Frequency given Displacement of Body?
The Natural Circular Frequency given Displacement of Body formula is defined as a scalar measure of rotation rate is calculated using Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period. To calculate Natural Circular Frequency given Displacement of Body, you need Displacement of Body (sbody), Maximum Displacement (x) & Time Period (tp). With our tool, you need to enter the respective value for Displacement of Body, Maximum Displacement & Time Period 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 Displacement of Body, Maximum Displacement & Time Period. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Frequency = Natural Circular Frequency/(2*pi)
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