Frequency Constant for Damped Vibrations given Circular Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2)
a = sqrt(ωn^2-ωd^2)
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
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Circular Damped Frequency - Circular Damped Frequency refers to the angular displacement per unit time.
STEP 1: Convert Input(s) to Base Unit
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Circular Damped Frequency: 6 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
a = sqrt(ωn^2-ωd^2) --> sqrt(21^2-6^2)
Evaluating ... ...
a = 20.1246117974981
STEP 3: Convert Result to Output's Unit
20.1246117974981 Hertz --> No Conversion Required
FINAL ANSWER
20.1246117974981 20.12461 Hertz <-- Frequency Constant for Calculation
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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10+ Under Damping Calculators

Periodic Time of Vibration
Go Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2))
Frequency of Damped Vibration
Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)
Circular Damped Frequency
Go Circular Damped Frequency = sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)
Periodic Time of Vibration using Natural Frequency
Go Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))
Frequency of Damped Vibration using Natural Frequency
Go Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
Displacement of Mass from Mean Position
Go Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period)
Frequency of Undamped Vibration
Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)
Frequency Constant for Damped Vibrations given Circular Frequency
Go Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2)
Circular Damped Frequency given Natural Frequency
Go Circular Damped Frequency = sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
Frequency Constant for Damped Vibrations
Go Frequency Constant for Calculation = Damping Coefficient/Mass Suspended from Spring

Frequency Constant for Damped Vibrations given Circular Frequency Formula

Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2)
a = sqrt(ωn^2-ωd^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 Constant for Damped Vibrations given Circular Frequency?

Frequency Constant for Damped Vibrations given Circular Frequency calculator uses Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2) to calculate the Frequency Constant for Calculation, Frequency Constant for Damped Vibrations given Circular Frequency is defined as the rate of change of the velocity of an object with respect to time. Frequency Constant for Calculation is denoted by a symbol.

How to calculate Frequency Constant for Damped Vibrations given Circular Frequency using this online calculator? To use this online calculator for Frequency Constant for Damped Vibrations given Circular Frequency, enter Natural Circular Frequency n) & Circular Damped Frequency d) and hit the calculate button. Here is how the Frequency Constant for Damped Vibrations given Circular Frequency calculation can be explained with given input values -> 20.12461 = sqrt(21^2-6^2).

FAQ

What is Frequency Constant for Damped Vibrations given Circular Frequency?
Frequency Constant for Damped Vibrations given Circular Frequency is defined as the rate of change of the velocity of an object with respect to time and is represented as a = sqrt(ωn^2-ωd^2) or Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2). Natural Circular Frequency is a scalar measure of rotation rate & Circular Damped Frequency refers to the angular displacement per unit time.
How to calculate Frequency Constant for Damped Vibrations given Circular Frequency?
Frequency Constant for Damped Vibrations given Circular Frequency is defined as the rate of change of the velocity of an object with respect to time is calculated using Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2). To calculate Frequency Constant for Damped Vibrations given Circular Frequency, you need Natural Circular Frequency n) & Circular Damped Frequency d). With our tool, you need to enter the respective value for Natural Circular Frequency & Circular Damped 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 Constant for Calculation?
In this formula, Frequency Constant for Calculation uses Natural Circular Frequency & Circular Damped Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Frequency Constant for Calculation = Damping Coefficient/Mass Suspended from Spring
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