Resonant Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
ωr = ωn*sqrt(1-2*ζ^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
Resonant Frequency - (Measured in Hertz) - Resonant Frequency is the oscillation of a system at its natural or unforced resonance.
Natural Frequency of Oscillation - (Measured in Hertz) - The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
STEP 1: Convert Input(s) to Base Unit
Natural Frequency of Oscillation: 23 Hertz --> 23 Hertz No Conversion Required
Damping Ratio: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ωr = ωn*sqrt(1-2*ζ^2) --> 23*sqrt(1-2*0.1^2)
Evaluating ... ...
ωr = 22.7688383542068
STEP 3: Convert Result to Output's Unit
22.7688383542068 Hertz --> No Conversion Required
FINAL ANSWER
22.7688383542068 22.76884 Hertz <-- Resonant Frequency
(Calculation completed in 00.004 seconds)

Credits

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Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
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Fundamental Parameters Calculators

Angle of Asymptotes
​ Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))
Bandwidth Frequency given Damping Ratio
​ Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
Closed Loop Negative Feedback Gain
​ Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
Closed Loop Gain
​ Go Closed-Loop Gain = 1/Feedback Factor

Control System Design Calculators

Bandwidth Frequency given Damping Ratio
​ Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
First Peak Undershoot
​ Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
​ Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Delay Time
​ Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Modelling Parameters Calculators

Damping Ratio or Damping Factor
​ Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
​ Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)
Resonant Frequency
​ Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Resonant Peak
​ Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Resonant Frequency Formula

Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
ωr = ωn*sqrt(1-2*ζ^2)

Why is resonant frequency important?

In the case of resonance, the deflection of the oscillation becomes larger. In acoustics, a higher amplitude of sound waves means a higher sound pressure and thus a higher volume. Resonant frequencies are generally undesirable for loudspeakers.

How to Calculate Resonant Frequency?

Resonant Frequency calculator uses Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2) to calculate the Resonant Frequency, Resonant Frequency formula is defined as the frequency at which the magnitude of the frequency response has peak value for the first time. Resonant Frequency is denoted by ωr symbol.

How to calculate Resonant Frequency using this online calculator? To use this online calculator for Resonant Frequency, enter Natural Frequency of Oscillation n) & Damping Ratio (ζ) and hit the calculate button. Here is how the Resonant Frequency calculation can be explained with given input values -> 22.76884 = 23*sqrt(1-2*0.1^2).

FAQ

What is Resonant Frequency?
Resonant Frequency formula is defined as the frequency at which the magnitude of the frequency response has peak value for the first time and is represented as ωr = ωn*sqrt(1-2*ζ^2) or Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2). The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position & Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
How to calculate Resonant Frequency?
Resonant Frequency formula is defined as the frequency at which the magnitude of the frequency response has peak value for the first time is calculated using Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2). To calculate Resonant Frequency, you need Natural Frequency of Oscillation n) & Damping Ratio (ζ). With our tool, you need to enter the respective value for Natural Frequency of Oscillation & Damping Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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