Calculator A to Z

Time Response of Critically Damped System Calculator

Engineering
Chemistry
Financial
Health
Math
Physics
Playground
✖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.ⓘ Natural Frequency of Oscillation [ωn]
+10%
-10%
✖Time Period for Oscillations is the time taken by a complete cycle of the wave to pass a particular interval.ⓘ Time Period for Oscillations [T]
+10%
-10%
✖Time response for second order system is defined as the response of a second order system towards any applied input.ⓘ Time Response of Critically Damped System [Ct]
⎘ Copy
👎
Formula
✖

Time Response of Critically Damped System

Formula
`"C"_{"t"} = 1-e^(-"ω"_{"n"}*"T")-(e^(-"ω"_{"n"}*"T")*"ω"_{"n"}*"T")`

Example
`"0.858732"=1-e^(-"23Hz"*"0.15s")-(e^(-"23Hz"*"0.15s")*"23Hz"*"0.15s")`

Calculator
LaTeX
Reset
👍

Time Response of Critically Damped System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
Ct = 1-e^(-ωn*T)-(e^(-ωn*T)*ωn*T)
This formula uses 1 Constants, 3 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
Time Response for Second Order System - Time response for second order system is defined as the response of a second order system towards any applied input.
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.
Time Period for Oscillations - (Measured in Second) - Time Period for Oscillations is the time taken by a complete cycle of the wave to pass a particular interval.
STEP 1: Convert Input(s) to Base Unit
Natural Frequency of Oscillation: 23 Hertz --> 23 Hertz No Conversion Required
Time Period for Oscillations: 0.15 Second --> 0.15 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ct = 1-e^(-ωn*T)-(e^(-ωn*T)*ωn*T) --> 1-e^(-23*0.15)-(e^(-23*0.15)*23*0.15)
Evaluating ... ...
Ct = 0.858731918117598
STEP 3: Convert Result to Output's Unit
0.858731918117598 --> No Conversion Required
FINAL ANSWER
0.858731918117598 ≈ 0.858732 <-- Time Response for Second Order System
(Calculation completed in 00.004 seconds)
You are here -
Home » Engineering » Electronics » Control System » Second Order System » Time Response of Critically Damped System

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Team Softusvista
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1100+ more calculators!

17 Second Order System Calculators

Time Response in Overdamped Case
Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Time Response of Critically Damped System
Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
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))
Rise Time given Damping Ratio
Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Time Response in Undamped Case
Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))
Number of Oscillations
Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Delay Time
Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Time Period of Oscillations
Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Peak Time
Go Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Go Rise Time = 1.5*Delay Time

16 Second Order System Calculators

Time Response in Overdamped Case
Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Time Response of Critically Damped System
Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
Rise Time given Damping Ratio
Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Time Response in Undamped Case
Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))
Number of Oscillations
Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Delay Time
Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Time Period of Oscillations
Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Peak Time
Go Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Go Rise Time = 1.5*Delay Time

25 Control System Design Calculators

Time Response in Overdamped Case
Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Time Response of Critically Damped System
Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
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))
Rise Time given Damping Ratio
Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Time Response in Undamped Case
Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Number of Oscillations
Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Delay Time
Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Time Period of Oscillations
Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Setting Time when Tolerance is 2 Percent
Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Peak Time
Go Peak Time = pi/Damped Natural Frequency
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)
Rise Time given Delay Time
Go Rise Time = 1.5*Delay Time

Time Response of Critically Damped System Formula

Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
Ct = 1-e^(-ωn*T)-(e^(-ωn*T)*ωn*T)

What is the settling time for a unit step input?

Settling time (ts) is the time required for a response to become steady. It is defined as the time required by the response to reach and steady within specified range of 2 % to 5 % of its final value.

How to Calculate Time Response of Critically Damped System?

Time Response of Critically Damped System calculator uses Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations) to calculate the Time Response for Second Order System, Time Response of Critically Damped System occurs when the damping factor/damping ratio is equal to 1 after the process of damping takes place. Time Response for Second Order System is denoted by Ct symbol.

How to calculate Time Response of Critically Damped System using this online calculator? To use this online calculator for Time Response of Critically Damped System, enter Natural Frequency of Oscillation (ωn) & Time Period for Oscillations (T) and hit the calculate button. Here is how the Time Response of Critically Damped System calculation can be explained with given input values -> 0.858732 = 1-e^(-23*0.15)-(e^(-23*0.15)*23*0.15).

FAQ

What is Time Response of Critically Damped System?
Time Response of Critically Damped System occurs when the damping factor/damping ratio is equal to 1 after the process of damping takes place and is represented as Ct = 1-e^(-ωn*T)-(e^(-ωn*T)*ωn*T) or Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations). 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 & Time Period for Oscillations is the time taken by a complete cycle of the wave to pass a particular interval.
How to calculate Time Response of Critically Damped System?
Time Response of Critically Damped System occurs when the damping factor/damping ratio is equal to 1 after the process of damping takes place is calculated using Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations). To calculate Time Response of Critically Damped System, you need Natural Frequency of Oscillation (ωn) & Time Period for Oscillations (T). With our tool, you need to enter the respective value for Natural Frequency of Oscillation & Time Period for Oscillations 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 Response for Second Order System?
In this formula, Time Response for Second Order System uses Natural Frequency of Oscillation & Time Period for Oscillations. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
  • Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
  • Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
  • Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
  • Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
  • Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
About | Contact | Disclaimer | Terms | Privacy Policy
© 2016-2024 A softusvista inc. venture!



Home
FREE PDFs
🔍 Search

Categories

Share
Let Others Know
✖
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!