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
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 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

### Bandwidth frequency Formula

Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+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
Resonant frequency GO

## What is bandwidth?

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth.

## How to Calculate Bandwidth frequency?

Bandwidth frequency calculator uses Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+2)) to calculate the Bandwidth frequency, Bandwidth frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value. Bandwidth frequency and is denoted by ωb symbol.

How to calculate Bandwidth frequency using this online calculator? To use this online calculator for Bandwidth frequency, enter Damping ratio (ζ) and Natural frequency n) and hit the calculate button. Here is how the Bandwidth frequency calculation can be explained with given input values -> 15.42771 = 10*sqrt(1-2*(0.1)^2+sqrt(4*(0.1)^4-4*(0.1)^2+2)).

### FAQ

What is Bandwidth frequency?
Bandwidth frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value and is represented as ωbn*sqrt(1-2*(ζ)^2+sqrt(4*(ζ)^4-4*(ζ)^2+2)) or Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+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 Bandwidth frequency?
Bandwidth frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value is calculated using Bandwidth frequency=Natural frequency*sqrt(1-2*(Damping ratio)^2+sqrt(4*(Damping ratio)^4-4*(Damping ratio)^2+2)). To calculate Bandwidth 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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