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First Peak Overshoot Formula

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Peak Overshoot is a straight way difference between the magnitude of the highest peak of time response and the magnitude of its steady state. Check FAQs

M o = e^{- \frac{π \cdot ζ}{\sqrt{1 - ζ^{2}}}}

M_o - Peak Overshoot?ζ - Damping Ratio?π - Archimedes' constant?

First Peak Overshoot Example

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Here is how the First Peak Overshoot equation looks like with Values.

Here is how the First Peak Overshoot equation looks like with Units.

Here is how the First Peak Overshoot equation looks like.

0.7292 = e^{- \frac{3.1416 \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

0.7292 = e^{- \frac{3.1416 \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

0.7292 = e^{- \frac{3.1416 \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

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First Peak Overshoot Solution

Follow our step by step solution on how to calculate First Peak Overshoot?

FIRST Step Consider the formula

M o = e^{- \frac{π \cdot ζ}{\sqrt{1 - ζ^{2}}}}

Next Step Substitute values of Variables

∴

M o = e^{- \frac{π \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

Next Step Substitute values of Constants

∴

M o = e^{- \frac{3.1416 \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

Next Step Prepare to Evaluate

∴

M o = e^{- \frac{3.1416 \cdot 0.1}{\sqrt{1 - {0.1}^{2}}}}

Next Step Evaluate

∴

M o = 0.729247614287671

LAST Step Rounding Answer

∴

M o = 0.7292

First Peak Overshoot Formula Elements

Variables

Constants

Functions

Peak Overshoot

Peak Overshoot is a straight way difference between the magnitude of the highest peak of time response and the magnitude of its steady state.

Symbol: M_o

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peak 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 Second Order System category

Go Bandwidth Frequency given Damping Ratio

f b = ω n \cdot (\sqrt{1 - (2 \cdot ζ^{2})} + \sqrt{ζ^{4} - (4 \cdot ζ^{2}) + 2})

Go Delay Time

t d = \frac{1 + (0.7 \cdot ζ)}{ω n}

Go First Peak Undershoot

M u = e^{- \frac{2 \cdot ζ \cdot π}{\sqrt{1 - ζ^{2}}}}

Go Number of Oscillations

n = \frac{t s \cdot ω d}{2 \cdot π}

How to Evaluate First Peak Overshoot?

First Peak Overshoot evaluator uses Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2))) to evaluate the Peak Overshoot, First Peak Overshoot is defined as the deviation of the response at peak time from the final value of response. It is the case when n is any odd integer. Peak Overshoot is denoted by M_o symbol.

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

FAQs on First Peak Overshoot

What is the formula to find First Peak Overshoot?

The formula of First Peak Overshoot is expressed as Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2))). Here is an example- 0.729248 = e^(-(pi*0.1)/(sqrt(1-0.1^2))).

How to calculate First Peak Overshoot?

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

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