National Institute of Information Technology (NIIT), Neemrana
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## < 11 Other formulas that you can solve using the same Inputs

Time response in overdamped case
Time response in overdamped case=1-(e^(-(Damping ratio-sqrt((Damping ratio^2)-1))*(Natural frequency*Time period of oscillations))/(2*sqrt((Damping ratio^2)-1)*(Damping ratio-sqrt((Damping ratio^2)-1)))) GO
Time response in critically damped case
Time response in critically damped case=1-e^(-(Natural frequency*Time period of oscillations))*(1+(Natural frequency*Time period of oscillations)) GO
Bandwidth frequency
Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+2)) GO
Maximum Overshoot
Maximum overshoot=2.71^(-(Damping ratio*Damped natural frequency)/(sqrt(1-(Damping ratio)^2))) GO
Time response in undamped case
Time response in undamped case=1-cos(Natural frequency*Time period of oscillations) GO
Time constant
Time constant=1/((Damping ratio-sqrt((Damping ratio)^2-1))*Natural frequency) GO
Damped natural frequency
Damped natural frequency=Natural frequency*sqrt(1-(Damping ratio)^2) GO
Resonant peak
Resonant peak=1/((2*Damping ratio)*sqrt(1-(Damping ratio)^2)) GO
Setting time when tolerance is 5%
Setting time=3/(Damping ratio*Damped natural frequency) GO
Setting time when tolerance is 2%
Setting time=4/(Damping ratio*Damped natural frequency) GO
Delay time
Delay time=(1+(0.7*Damping ratio))/Natural frequency GO

### Resonant frequency Formula

Resonant frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2)
More formulas
Transfer Function for Open Loop System GO
Delay time GO
Damped natural frequency GO
Damping ratio / Damping factor GO
Peak time GO
Setting time when tolerance is 5% GO
Setting time when tolerance is 2% GO
Rise time GO
Maximum Overshoot GO
Time period of oscillations GO
Number of oscillations GO
Rise time when delay time is given GO
Resonant peak GO
Bandwidth frequency GO

## What is Resonant frequency?

Resonant frequency is the oscillation of a system at its natural or unforced resonance. Resonance occurs when a system is able to store and easily transfer energy between different storage modes, such as Kinetic energy or Potential energy as you would find with a simple pendulum. Most systems have one resonant frequency and multiple harmonic frequencies that get progressively lower in amplitude as they move away from the center.

## How to Calculate Resonant frequency?

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

How to calculate Resonant frequency using this online calculator? To use this online calculator for Resonant frequency, enter Damping ratio (ζ) and Natural frequency n) and hit the calculate button. Here is how the Resonant frequency calculation can be explained with given input values -> 9.899495 = 10*sqrt(1-2*(0.1)^2).

### FAQ

What is Resonant frequency?
Resonant frequency is the frequency at which the magnitude of the frequency response has peak value for the first time. and is represented as ωrn*sqrt(1-2*(ζ)^2) or Resonant frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2). Damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance and Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.
How to calculate Resonant frequency?
Resonant frequency is the frequency at which the magnitude of the frequency response has peak value for the first time. is calculated using Resonant frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2). To calculate Resonant frequency, you need Damping ratio (ζ) and Natural frequency n). With our tool, you need to enter the respective value for Damping ratio and Natural frequency 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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