Damping Ratio given Percentage Overshoot Calculator

Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2)
ζ = -ln(%_o/100)/sqrt(pi^2+ln(%_o/100)^2)
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
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

Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Percentage Overshoot - Percentage Overshoot refers to an output exceeding its final, steady-state value.

STEP 1: Convert Input(s) to Base Unit

Percentage Overshoot: 72.9 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ = -ln(%_o/100)/sqrt(pi^2+ln(%_o/100)^2) --> -ln(72.9/100)/sqrt(pi^2+ln(72.9/100)^2)

Evaluating ... ...

ζ = 0.100106480562248

STEP 3: Convert Result to Output's Unit

0.100106480562248 --> No Conversion Required

FINAL ANSWER

0.100106480562248 ≈ 0.100106 <-- 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 Negative 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 Positive 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 Percentage Overshoot Formula

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

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 Percentage Overshoot?

Damping Ratio given Percentage Overshoot calculator uses Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2) to calculate the Damping Ratio, The Damping Ratio given Percentage Overshoot formula is 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 Percentage Overshoot using this online calculator? To use this online calculator for Damping Ratio given Percentage Overshoot, enter Percentage Overshoot (%_o) and hit the calculate button. Here is how the Damping Ratio given Percentage Overshoot calculation can be explained with given input values -> 0.100106 = -ln(72.9/100)/sqrt(pi^2+ln(72.9/100)^2).

FAQ

What is Damping Ratio given Percentage Overshoot?

The Damping Ratio given Percentage Overshoot formula is 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 = -ln(%_o/100)/sqrt(pi^2+ln(%_o/100)^2) or Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2). Percentage Overshoot refers to an output exceeding its final, steady-state value.

How to calculate Damping Ratio given Percentage Overshoot?

The Damping Ratio given Percentage Overshoot formula is 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 = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2). To calculate Damping Ratio given Percentage Overshoot, you need Percentage Overshoot (%_o). With our tool, you need to enter the respective value for Percentage Overshoot 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 Percentage Overshoot. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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