Time constant Calculator

Category	Engineering ↺
Engineering	Electronics ↺
Electronics	Control Systems ↺
Control-Systems	Time response of 2nd order system ↺

✖Damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.ⓘ Damping ratio [ζ]			+10% -10%
✖Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.ⓘ Natural frequency [ω_n]			+10% -10%

✖Time constant of the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate.ⓘ Time constant [T]

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Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 50+ more calculators!

< 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

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

< 4 Other formulas that calculate the same Output

Time Constant When The Frequency Is Given

Time constant=1/(2*frequency*pi*Capacitance) GO

Time Constant For The RC Circuit When The Capacitance Is Given

Time constant=Resistance*Capacitance GO

Time Constant For The RC Circuit When Resistance Is Given

Time constant=Resistance*Capacitance GO

Time Constant For The RC Circuit When The Inductance Is Given

Time constant=Inductance/Resistance GO

Time constant Formula

Time constant=1/((Damping ratio-sqrt((Damping ratio)^2-1))*Natural frequency)

More formulas

Time response in undamped case GO

Time response in critically damped case GO

Time response in overdamped case GO

Number of Asymptotes GO

Angle of asymptotes GO

What is time constant in second order system?

The second order process time constant is the speed that the output response reaches a new steady state condition. An overdamped second order system may be the combination of first two order systems. The time constant of undamped system is the greatest followed by the time constant of overdamped system, underdamped system and lastly critically damped system.

How to Calculate Time constant?

Time constant calculator uses Time constant=1/((Damping ratio-sqrt((Damping ratio)^2-1))*Natural frequency) to calculate the Time constant, Time constant of the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate. Time constant and is denoted by T symbol.

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

FAQ

What is Time constant?

Time constant of the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate and is represented as T=1/((ζ-sqrt((ζ)^2-1))*ω_n) or Time constant=1/((Damping ratio-sqrt((Damping ratio)^2-1))*Natural frequency). 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 Time constant?

Time constant of the response represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate is calculated using Time constant=1/((Damping ratio-sqrt((Damping ratio)^2-1))*Natural frequency). To calculate Time constant, you need Damping ratio (ζ) and Natural frequency (ω_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.

How many ways are there to calculate Time constant?

In this formula, Time constant uses Damping ratio and Natural frequency. We can use 4 other way(s) to calculate the same, which is/are as follows -

Time constant=Resistance*Capacitance
Time constant=Resistance*Capacitance
Time constant=Inductance/Resistance
Time constant=1/(2*frequency*pi*Capacitance)

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