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Percentage Overshoot Formula

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Percentage Overshoot refers to an output exceeding its final, steady-state value. Check FAQs

% o = 100 \cdot (e^{\frac{- ζ \cdot π}{\sqrt{1 - (ζ^{2})}}})

%_o - Percentage Overshoot?ζ - Damping Ratio?π - Archimedes' constant?

Percentage Overshoot Example

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Here is how the Percentage Overshoot equation looks like with Values.

Here is how the Percentage Overshoot equation looks like with Units.

Here is how the Percentage Overshoot equation looks like.

72.9248 = 100 \cdot (e^{\frac{- 0.1 \cdot 3.1416}{\sqrt{1 - ({0.1}^{2})}}})

72.9248 = 100 \cdot (e^{\frac{- 0.1 \cdot 3.1416}{\sqrt{1 - ({0.1}^{2})}}})

72.9248 = 100 \cdot (e^{\frac{- 0.1 \cdot 3.1416}{\sqrt{1 - ({0.1}^{2})}}})

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Percentage Overshoot Solution

Follow our step by step solution on how to calculate Percentage Overshoot?

FIRST Step Consider the formula

% o = 100 \cdot (e^{\frac{- ζ \cdot π}{\sqrt{1 - (ζ^{2})}}})

Next Step Substitute values of Variables

∴

% o = 100 \cdot (e^{\frac{- 0.1 \cdot π}{\sqrt{1 - ({0.1}^{2})}}})

Next Step Substitute values of Constants

∴

% o = 100 \cdot (e^{\frac{- 0.1 \cdot 3.1416}{\sqrt{1 - ({0.1}^{2})}}})

Next Step Prepare to Evaluate

∴

% o = 100 \cdot (e^{\frac{- 0.1 \cdot 3.1416}{\sqrt{1 - ({0.1}^{2})}}})

Next Step Evaluate

∴

% o = 72.9247614287671

LAST Step Rounding Answer

∴

% o = 72.9248

Percentage Overshoot Formula Elements

Variables

Constants

Functions

Percentage Overshoot

Percentage Overshoot refers to an output exceeding its final, steady-state value.

Symbol: %_o

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Percentage Overshoot

Damping Ratio

Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Ratio

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in Fundamental Parameters category

Go Damping Ratio or Damping Factor

ζ = \frac{c}{2 \cdot \sqrt{m \cdot K spring}}

Go Damped Natural Frequency

ω d = ω n \cdot \sqrt{1 - ζ^{2}}

Go Resonant Peak

M r = \frac{1}{2 \cdot ζ \cdot \sqrt{1 - ζ^{2}}}

Go Resonant Frequency

ω r = ω n \cdot \sqrt{1 - 2 \cdot ζ^{2}}

How to Evaluate Percentage Overshoot?

Percentage Overshoot evaluator uses Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))) to evaluate the Percentage Overshoot, Percentage Overshoot formula is defined as the maximum peak value of the response curve measured from the desired response of the system. Percentage Overshoot is denoted by %_o symbol.

How to evaluate Percentage Overshoot using this online evaluator? To use this online evaluator for Percentage Overshoot, enter Damping Ratio (ζ) and hit the calculate button.

FAQs on Percentage Overshoot

What is the formula to find Percentage Overshoot?

The formula of Percentage Overshoot is expressed as Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))). Here is an example- 72.92476 = 100*(e^((-0.1*pi)/(sqrt(1-(0.1^2))))).

How to calculate Percentage Overshoot?

With Damping Ratio (ζ) we can find Percentage Overshoot using the formula - Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2))))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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