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First Peak Undershoot Formula

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

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

M_u - Peak Undershoot?ζ - Damping Ratio?π - Archimedes' constant?

First Peak Undershoot Example

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

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

Here is how the First Peak Undershoot equation looks like.

0.5318 = e^{- \frac{2 \cdot 0.1 \cdot 3.1416}{\sqrt{1 - {0.1}^{2}}}}

0.5318 = e^{- \frac{2 \cdot 0.1 \cdot 3.1416}{\sqrt{1 - {0.1}^{2}}}}

0.5318 = e^{- \frac{2 \cdot 0.1 \cdot 3.1416}{\sqrt{1 - {0.1}^{2}}}}

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First Peak Undershoot Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

M u = 0.53180208294426

LAST Step Rounding Answer

∴

M u = 0.5318

First Peak Undershoot Formula Elements

Variables

Constants

Functions

Peak Undershoot

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

Symbol: M_u

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Peak Undershoot

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 Overshoot

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

Go Number of Oscillations

n = \frac{t s \cdot ω d}{2 \cdot π}

How to Evaluate First Peak Undershoot?

First Peak Undershoot evaluator uses Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2))) to evaluate the Peak Undershoot, The First Peak Undershoot formula is defined as maximum deviation less than the steady state value in the 2nd order system response when n is equal to 2. Peak Undershoot is denoted by M_u symbol.

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

FAQs on First Peak Undershoot

What is the formula to find First Peak Undershoot?

The formula of First Peak Undershoot is expressed as Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2))). Here is an example- 0.531802 = e^(-(2*0.1*pi)/(sqrt(1-0.1^2))).

How to calculate First Peak Undershoot?

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

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