Damping Ratio given Critical Damping Calculator

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Fundamental Parameters

Second Order System

✖Actual Damping in a control system refers to the level of damping present in the system as a result of all the physical and electrical components that make up the system.ⓘ Actual Damping [C]			+10% -10%
✖Critical Damping refers to the amount of damping required in a system to return to its equilibrium state as quickly as possible without overshooting.ⓘ Critical Damping [C_c]			+10% -10%

✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio given Critical Damping [ζ]

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Formula

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Damping Ratio given Critical Damping

Formula

`"ζ" = "C"/"C"_{"c"}`

Example

`"0.100334"="0.6"/"5.98"`

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Damping Ratio given Critical Damping Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damping Ratio = Actual Damping/Critical Damping
ζ = C/C_c
This formula uses 3 Variables

Variables Used

Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Actual Damping - Actual Damping in a control system refers to the level of damping present in the system as a result of all the physical and electrical components that make up the system.
Critical Damping - Critical Damping refers to the amount of damping required in a system to return to its equilibrium state as quickly as possible without overshooting.

STEP 1: Convert Input(s) to Base Unit

Actual Damping: 0.6 --> No Conversion Required
Critical Damping: 5.98 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ = C/C_c --> 0.6/5.98

Evaluating ... ...

ζ = 0.100334448160535

STEP 3: Convert Result to Output's Unit

0.100334448160535 --> No Conversion Required

FINAL ANSWER

0.100334448160535 ≈ 0.100334 <-- Damping Ratio

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology,Roorlee (IITR), Roorkee

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< 19 Fundamental Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

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))

Damping Ratio given Percentage Overshoot

Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Closed Loop Positive Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1- (Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Negative Feedback Gain

Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*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)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Damping Ratio given Critical Damping

Go Damping Ratio = Actual Damping/Critical Damping

Closed Loop Gain

Go Closed-Loop Gain = 1/Feedback Factor

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

< 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

< 12 Modelling Parameters Calculators

Angle of Asymptotes

Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

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))

Damping Ratio given Percentage Overshoot

Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Damping Ratio or Damping Factor

Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))

Damped Natural Frequency

Go Damped Natural Frequency = Natural Frequency of Oscillation*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)

Resonant Peak

Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Damping Ratio given Critical Damping

Go Damping Ratio = Actual Damping/Critical Damping

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Damping Ratio given Critical Damping Formula

Damping Ratio = Actual Damping/Critical Damping
ζ = C/C_c

How the values of actual damping and critical damping affects the system?

If the actual damping ratio is greater than the critical damping ratio, the system is said to be overdamped, which means the system response is slow and it takes a long time to reach the equilibrium state after a disturbance. On the other hand, if the actual damping ratio is less than the critical damping ratio, the system is said to be underdamped and the system will have oscillations before reaching the equilibrium state.

How is damping ratio used?

To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping required to reach critical damping. The formula for the damping ratio is used for the mass-spring-damper model.

How to Calculate Damping Ratio given Critical Damping?

Damping Ratio given Critical Damping calculator uses Damping Ratio = Actual Damping/Critical Damping to calculate the Damping Ratio, Damping Ratio given Critical Damping is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. Damping Ratio is denoted by ζ symbol.

How to calculate Damping Ratio given Critical Damping using this online calculator? To use this online calculator for Damping Ratio given Critical Damping, enter Actual Damping (C) & Critical Damping (C_c) and hit the calculate button. Here is how the Damping Ratio given Critical Damping calculation can be explained with given input values -> 0.100334 = 0.6/5.98.

FAQ

What is Damping Ratio given Critical Damping?

Damping Ratio given Critical Damping is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator and is represented as ζ = C/C_c or Damping Ratio = Actual Damping/Critical Damping. Actual Damping in a control system refers to the level of damping present in the system as a result of all the physical and electrical components that make up the system & Critical Damping refers to the amount of damping required in a system to return to its equilibrium state as quickly as possible without overshooting.

How to calculate Damping Ratio given Critical Damping?

Damping Ratio given Critical Damping is defined as a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator is calculated using Damping Ratio = Actual Damping/Critical Damping. To calculate Damping Ratio given Critical Damping, you need Actual Damping (C) & Critical Damping (C_c). With our tool, you need to enter the respective value for Actual Damping & Critical Damping 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 Damping Ratio?

In this formula, Damping Ratio uses Actual Damping & Critical Damping. We can use 6 other way(s) to calculate the same, which is/are as follows -

Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)

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