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Angular Frequency Calculator

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Elements of Vibration Forced Vibration Free Vibration of Single DOF Undamped Torsional System Undamped Free Vibration

✖Spring Stiffness is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.ⓘ Spring Stiffness [k']			+10% -10%
✖Mass Attached to Spring is the amount of mass attached to a spring in a mechanical vibration system, affecting the vibration's frequency and amplitude.ⓘ Mass Attached to Spring [m']			+10% -10%

✖Angular Frequency is the number of oscillations or cycles per unit time of a vibrating system, characterizing its mechanical vibration.ⓘ Angular Frequency [ω']

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Angular Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring)
ω' = sqrt(k'/m')
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Angular Frequency - (Measured in Radian per Second) - Angular Frequency is the number of oscillations or cycles per unit time of a vibrating system, characterizing its mechanical vibration.
Spring Stiffness - (Measured in Newton per Meter) - Spring Stiffness is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.
Mass Attached to Spring - (Measured in Kilogram) - Mass Attached to Spring is the amount of mass attached to a spring in a mechanical vibration system, affecting the vibration's frequency and amplitude.

STEP 1: Convert Input(s) to Base Unit

Spring Stiffness: 10.4 Newton per Meter --> 10.4 Newton per Meter No Conversion Required
Mass Attached to Spring: 2.6 Kilogram --> 2.6 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω' = sqrt(k'/m') --> sqrt(10.4/2.6)

Evaluating ... ...

ω' = 2

STEP 3: Convert Result to Output's Unit

2 Radian per Second --> No Conversion Required

FINAL ANSWER

2 Radian per Second <-- Angular Frequency

(Calculation completed in 00.004 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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< Elements of Vibration Calculators

Velocity of Body in Simple Harmonic Motion

LaTeX Go Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds)

Magnitude of Acceleration of Body in Simple Harmonic Motion

LaTeX Go Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)

Displacement of Body in Simple Harmonic Motion

LaTeX Go Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds)

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement

LaTeX Go Acceleration = Angular Velocity^2*Displacement of Body

Angular Frequency Formula

LaTeX Go

Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring)
ω' = sqrt(k'/m')

What is Angular Frequency?

For a sinusoidal wave, the angular frequency refers to the angular displacement of any element of the wave per unit time or the rate of change of the phase of the waveform. It is represented by ω.

How to Calculate Angular Frequency?

Angular Frequency calculator uses Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring) to calculate the Angular Frequency, Angular Frequency formula is defined as a measure of the number of oscillations or rotations made by an object per unit time, characterizing the frequency of mechanical vibrations in a system, providing insights into the system's dynamic behavior and stability. Angular Frequency is denoted by ω' symbol.

How to calculate Angular Frequency using this online calculator? To use this online calculator for Angular Frequency, enter Spring Stiffness (k') & Mass Attached to Spring (m') and hit the calculate button. Here is how the Angular Frequency calculation can be explained with given input values -> 2 = sqrt(10.4/2.6).

FAQ

What is Angular Frequency?

Angular Frequency formula is defined as a measure of the number of oscillations or rotations made by an object per unit time, characterizing the frequency of mechanical vibrations in a system, providing insights into the system's dynamic behavior and stability and is represented as ω' = sqrt(k'/m') or Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring). Spring Stiffness is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched & Mass Attached to Spring is the amount of mass attached to a spring in a mechanical vibration system, affecting the vibration's frequency and amplitude.

How to calculate Angular Frequency?

Angular Frequency formula is defined as a measure of the number of oscillations or rotations made by an object per unit time, characterizing the frequency of mechanical vibrations in a system, providing insights into the system's dynamic behavior and stability is calculated using Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring). To calculate Angular Frequency, you need Spring Stiffness (k') & Mass Attached to Spring (m'). With our tool, you need to enter the respective value for Spring Stiffness & Mass Attached to Spring 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 Angular Frequency?

In this formula, Angular Frequency uses Spring Stiffness & Mass Attached to Spring. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angular Frequency = 2*pi/Time Period SHM

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