Frequency of Damped Vibration using Natural Frequency Calculator

✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.ⓘ Frequency Constant for Calculation [a]			+10% -10%

✖Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.ⓘ Frequency of Damped Vibration using Natural Frequency [f]

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Frequency of Damped Vibration using Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
f = 1/(2*pi)*sqrt(ω_n^2-a^2)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

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.
Frequency Constant for Calculation - (Measured in Hertz) - The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.

STEP 1: Convert Input(s) to Base Unit

Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Frequency Constant for Calculation: 0.2 Hertz --> 0.2 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = 1/(2*pi)*sqrt(ω_n^2-a^2) --> 1/(2*pi)*sqrt(21^2-0.2^2)

Evaluating ... ...

f = 3.34210222535627

STEP 3: Convert Result to Output's Unit

3.34210222535627 Hertz --> No Conversion Required

FINAL ANSWER

3.34210222535627 ≈ 3.342102 Hertz <-- Frequency

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Frequency of Free Damped Vibrations Calculators

Condition for Critical Damping

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Damping Factor given Natural Frequency

LaTeX Go Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)

Critical Damping Coefficient

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency

Damping Factor

LaTeX Go Damping Ratio = Damping Coefficient/Critical Damping Coefficient

Frequency of Damped Vibration using Natural Frequency Formula

LaTeX Go

Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
f = 1/(2*pi)*sqrt(ω_n^2-a^2)

Why damping happens during vibration?

The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness. Damped vibration happens when the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped.

How to Calculate Frequency of Damped Vibration using Natural Frequency?

Frequency of Damped Vibration using Natural Frequency calculator uses Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2) to calculate the Frequency, Frequency of Damped Vibration using Natural Frequency formula is defined as a measure of the number of oscillations per unit time of an object under the influence of a damping force, providing insight into the vibrational characteristics of a system in a state of free damped vibration. Frequency is denoted by f symbol.

How to calculate Frequency of Damped Vibration using Natural Frequency using this online calculator? To use this online calculator for Frequency of Damped Vibration using Natural Frequency, enter Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a) and hit the calculate button. Here is how the Frequency of Damped Vibration using Natural Frequency calculation can be explained with given input values -> 3.342102 = 1/(2*pi)*sqrt(21^2-0.2^2).

FAQ

What is Frequency of Damped Vibration using Natural Frequency?

Frequency of Damped Vibration using Natural Frequency formula is defined as a measure of the number of oscillations per unit time of an object under the influence of a damping force, providing insight into the vibrational characteristics of a system in a state of free damped vibration and is represented as f = 1/(2*pi)*sqrt(ω_n^2-a^2) or Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2). Natural Circular Frequency is a scalar measure of rotation rate & The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.

How to calculate Frequency of Damped Vibration using Natural Frequency?

Frequency of Damped Vibration using Natural Frequency formula is defined as a measure of the number of oscillations per unit time of an object under the influence of a damping force, providing insight into the vibrational characteristics of a system in a state of free damped vibration is calculated using Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2). To calculate Frequency of Damped Vibration using Natural Frequency, you need Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a). With our tool, you need to enter the respective value for Natural Circular Frequency & Frequency Constant for Calculation 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 & Frequency Constant for Calculation. We can use 2 other way(s) to calculate the same, which is/are as follows -

Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)
Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)

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