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Time Response of Critically Damped System Calculator

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Second Order System Fundamental Parameters

✖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 [ω_n]			+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 [C_t]

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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)
C_t = 1-e^(-ω_n*T)-(e^(-ω_n*T)*ω_n*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

C_t = 1-e^(-ω_n*T)-(e^(-ω_n*T)*ω_n*T) --> 1-e^(-23*0.15)-(e^(-23*0.15)*23*0.15)

Evaluating ... ...

C_t = 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 00.020 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Second Order System Calculators

Bandwidth Frequency given Damping Ratio

LaTeX Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

< Second Order System Calculators

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Rise Time given Damped Natural Frequency

LaTeX Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Peak Time

LaTeX Go Peak Time = pi/Damped Natural Frequency

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

LaTeX Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Time Response of Critically Damped System Formula

LaTeX Go

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 C_t 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 (ω_n) & 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 C_t = 1-e^(-ω_n*T)-(e^(-ω_n*T)*ω_n*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 (ω_n) & 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 3 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))))

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