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Resonant Peak Formula

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Resonant Peak is the peak (maximum) value of the magnitude of frequency domain. It is denoted by M_r. Check FAQs

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

M_r - Resonant Peak?ζ - Damping Ratio?

Resonant Peak Example

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With units

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Here is how the Resonant Peak equation looks like with Values.

Here is how the Resonant Peak equation looks like with Units.

Here is how the Resonant Peak equation looks like.

5.0252 = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - {0.1}^{2}}}

5.0252 = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - {0.1}^{2}}}

5.0252 = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - {0.1}^{2}}}

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Resonant Peak Solution

Follow our step by step solution on how to calculate Resonant Peak?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

M r = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - {0.1}^{2}}}

Next Step Prepare to Evaluate

∴

M r = \frac{1}{2 \cdot 0.1 \cdot \sqrt{1 - {0.1}^{2}}}

Next Step Evaluate

∴

M r = 5.02518907629606

LAST Step Rounding Answer

∴

M r = 5.0252

Resonant Peak Formula Elements

Variables

Functions

Resonant Peak

Resonant Peak is the peak (maximum) value of the magnitude of frequency domain. It is denoted by M_r.

Symbol: M_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Resonant Peak

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

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 Frequency

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

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})

How to Evaluate Resonant Peak?

Resonant Peak evaluator uses Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)) to evaluate the Resonant Peak, Resonant Peak formula is defined as the peak (maximum) value of the magnitude of frequency domain. Resonant Peak is denoted by M_r symbol.

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

FAQs on Resonant Peak

What is the formula to find Resonant Peak?

The formula of Resonant Peak is expressed as Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)). Here is an example- 5.025189 = 1/(2*0.1*sqrt(1-0.1^2)).

How to calculate Resonant Peak?

With Damping Ratio (ζ) we can find Resonant Peak using the formula - Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)). This formula also uses Square Root (sqrt) function(s).

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