Damping Ratio given Percentage Overshoot Calculator

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✖Percentage Overshoot refers to an output exceeding its final, steady-state value.ⓘ Percentage Overshoot [PO]

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

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Formula

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Damping Ratio given Percentage Overshoot

Formula

`"ζ" = -ln("PO"/100)/ sqrt((pi^2)+ln("PO"/100)^2)`

Example

`"0.112808"=-ln("70"/100)/ sqrt((pi^2)+ln("70"/100)^2)`

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Damping Ratio given Percentage Overshoot Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - Natural logarithm function (base e), ln(Number)
sqrt - Squre root function, 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: 70 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ = -ln(PO/100)/ sqrt((pi^2)+ln(PO/100)^2) --> -ln(70/100)/ sqrt((pi^2)+ln(70/100)^2)

Evaluating ... ...

ζ = 0.112808450693581

STEP 3: Convert Result to Output's Unit

0.112808450693581 --> No Conversion Required

FINAL ANSWER

0.112808450693581 <-- Damping Ratio

(Calculation completed in 00.000 seconds)

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< 10+ Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

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Bandwidth Frequency given Damping Ratio

Formula

`"f"_{"b"} = "f"*((sqrt(1-(2*("ζ"^2))))+sqrt(("ζ"^4)-(4*("ζ"^2))+2))`

Example

`"54.96966Hz"="23Hz"*((sqrt(1-(2*("0.1"^2))))+sqrt(("0.1"^4)-(4*("0.1"^2))+2))`

Calculator

LaTeX

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

Angle of Asymptotes

✖

Angle of Asymptotes

Formula

`"ϕ"_{"k"} = (((2*"K")+1)*pi)/("P"-"Z")`

Example

`"951.4286°"=(((2*"18")+1)*pi)/("13"-"6")`

Calculator

LaTeX

Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)

Damping Ratio or Damping Factor

✖

Damping Ratio or Damping Factor

Formula

`"ζ" = "c"/(2*sqrt("M"*"K"_{"spring"}))`

Example

`"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))`

Calculator

LaTeX

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

Gain-bandwidth Product

✖

Gain-bandwidth Product

Formula

`"G.B" = "modulus"("A"_{"M"})*"BW"`

Example

`"56.16Hz"="modulus"("0.78")*"72b/s"`

Calculator

LaTeX

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid-band)*Amplifier Bandwidth

Damped Natural Frequency

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Damped Natural Frequency

Formula

`"ω"_{"d"} = "f"*(sqrt(1-("ζ")^2))`

Example

`"22.88471Hz"="23Hz"*(sqrt(1-("0.1")^2))`

Calculator

LaTeX

Go Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2))

Resonant Peak

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Resonant Peak

Formula

`"M"_{"r"} = 1/((2*"ζ")*sqrt(1-("ζ")^2))`

Example

`"5.025189"=1/((2*"0.1")*sqrt(1-("0.1")^2))`

Calculator

LaTeX

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

Resonant Frequency

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Resonant Frequency

Formula

`"ω"_{"r"} = "f"*sqrt(1-2*("ζ")^2)`

Example

`"22.76884Hz"="23Hz"*sqrt(1-2*("0.1")^2)`

Calculator

LaTeX

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

Number of Asymptotes

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Number of Asymptotes

Formula

`"N"_{"a"} = "P"-"Z"`

Example

`"7"="13"-"6"`

Calculator

LaTeX

Go Number of Asymptotes = Number of Poles-Number of Zeros

Transfer Function for Closed and Open Loop System

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Transfer Function for Closed and Open Loop System

Formula

`"G"_{"s"} = "C"_{"s"}/"R"_{"s"}`

Example

`"0.458333"="22"/"48"`

Calculator

LaTeX

Go Transfer Function = Output of System/Input of System

Closed-loop Gain

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Closed-loop Gain

Formula

`"A"_{"f"} = 1/"β"`

Example

`"0.25"=1/"4"`

Calculator

LaTeX

Go Gain-with-feedback = 1/Feedback Factor

Damping Ratio given Percentage Overshoot Formula

Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt((pi^2)+ln(Percentage Overshoot/100)^2)
ζ = -ln(PO/100)/ sqrt((pi^2)+ln(PO/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 (PO) and hit the calculate button. Here is how the Damping Ratio given Percentage Overshoot calculation can be explained with given input values -> 0.112808 = -ln(70/100)/ sqrt((pi^2)+ln(70/100)^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(PO/100)/ sqrt((pi^2)+ln(PO/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 (PO). 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 2 other way(s) to calculate the same, which is/are as follows -

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

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