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Time Response in Overdamped Case Calculator

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Second Order System Fundamental Parameters

✖Overdamping Ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.ⓘ Overdamping Ratio [ζ_over]			+10% -10%
✖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 in Overdamped Case [C_t]

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Time Response in Overdamped Case Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
C_t = 1-(e^(-(ζ_over-(sqrt((ζ_over^2)-1)))*(ω_n*T))/(2*sqrt((ζ_over^2)-1)*(ζ_over-sqrt((ζ_over^2)-1))))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Overdamping Ratio - Overdamping Ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.
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

Overdamping Ratio: 1.12 --> No Conversion Required
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^(-(ζ_over-(sqrt((ζ_over^2)-1)))*(ω_n*T))/(2*sqrt((ζ_over^2)-1)*(ζ_over-sqrt((ζ_over^2)-1)))) --> 1-(e^(-(1.12-(sqrt((1.12^2)-1)))*(23*0.15))/(2*sqrt((1.12^2)-1)*(1.12-sqrt((1.12^2)-1))))

Evaluating ... ...

C_t = 0.807466086195714

STEP 3: Convert Result to Output's Unit

0.807466086195714 --> No Conversion Required

FINAL ANSWER

0.807466086195714 ≈ 0.807466 <-- Time Response for Second Order System

(Calculation completed in 00.020 seconds)

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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 in Overdamped Case Formula

LaTeX Go

What is the time response in overdamped case?

The time response in overdamped system is the response that does not oscillate about the steady-state value but takes longer to reach steady-state than the critically damped case. For the value of ζ comparatively much greater than one, the effect of faster time constant on the time response can be neglected.

How to Calculate Time Response in Overdamped Case?

Time Response in Overdamped Case calculator uses 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)))) to calculate the Time Response for Second Order System, Time Response in Overdamped Case occurs when the damping factor/damping ratio is more than 1 during the process of damping. Time Response for Second Order System is denoted by C_t symbol.

How to calculate Time Response in Overdamped Case using this online calculator? To use this online calculator for Time Response in Overdamped Case, enter Overdamping Ratio (ζ_over), Natural Frequency of Oscillation (ω_n) & Time Period for Oscillations (T) and hit the calculate button. Here is how the Time Response in Overdamped Case calculation can be explained with given input values -> 0.807466 = 1-(e^(-(1.12-(sqrt((1.12^2)-1)))*(23*0.15))/(2*sqrt((1.12^2)-1)*(1.12-sqrt((1.12^2)-1)))).

FAQ

What is Time Response in Overdamped Case?

Time Response in Overdamped Case occurs when the damping factor/damping ratio is more than 1 during the process of damping and is represented as C_t = 1-(e^(-(ζ_over-(sqrt((ζ_over^2)-1)))*(ω_n*T))/(2*sqrt((ζ_over^2)-1)*(ζ_over-sqrt((ζ_over^2)-1)))) or 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)))). Overdamping Ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance, 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 in Overdamped Case?

Time Response in Overdamped Case occurs when the damping factor/damping ratio is more than 1 during the process of damping is calculated using 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)))). To calculate Time Response in Overdamped Case, you need Overdamping Ratio (ζ_over), Natural Frequency of Oscillation (ω_n) & Time Period for Oscillations (T). With our tool, you need to enter the respective value for Overdamping Ratio, 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 Overdamping Ratio, 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-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
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)
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)

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