 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
Resonant frequency
Resonant frequency=Natural frequency*sqrt(1-2*(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

### Damped natural frequency Formula

Damped natural frequency=Natural frequency*sqrt(1-(Damping ratio)^2)
More formulas
Transfer Function for Open Loop System GO
Delay time 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
Resonant frequency GO
Bandwidth frequency GO

## What is the characteristics of damped natural frequency?

The damped natural frequency is less than the undamped natural frequency, but for many practical cases the damping ratio is relatively small and hence the difference is negligible. Therefore, the damped and undamped description are often dropped when stating the natural frequency. For most structures the level of damping is such that the damped natural frequencies are very nearly equal to the undamped natural frequencies. Thus, if only the natural frequencies of the structure are required, damping can usually be neglected in the analysis. This is a significant simplification. Also, if the response of a structure at a frequency well away from a resonance is required, a similar simplification may be made in the analysis.

## How to Calculate Damped natural frequency?

Damped natural frequency calculator uses Damped natural frequency=Natural frequency*sqrt(1-(Damping ratio)^2) to calculate the Damped natural frequency, Damped natural frequency is a frequency if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency. Damped natural frequency and is denoted by ωd symbol.

How to calculate Damped natural frequency using this online calculator? To use this online calculator for Damped natural frequency, enter Damping ratio (ζ) and Natural frequency n) and hit the calculate button. Here is how the Damped natural frequency calculation can be explained with given input values -> 9.949874 = 10*sqrt(1-(0.1)^2).

### FAQ

What is Damped natural frequency?
Damped natural frequency is a frequency if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency and is represented as ωdn*sqrt(1-(ζ)^2) or Damped natural frequency=Natural frequency*sqrt(1-(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 Damped natural frequency?
Damped natural frequency is a frequency if a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency is calculated using Damped natural frequency=Natural frequency*sqrt(1-(Damping ratio)^2). To calculate Damped natural 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. Let Others Know