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Resonant Peak Calculator

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Fundamental Parameters Second Order System

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

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

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Resonant Peak Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
M_r = 1/(2*ζ*sqrt(1-ζ^2))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Resonant Peak - Resonant Peak is the peak (maximum) value of the magnitude of frequency domain. It is denoted by M_r.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

STEP 1: Convert Input(s) to Base Unit

Damping Ratio: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_r = 1/(2*ζ*sqrt(1-ζ^2)) --> 1/(2*0.1*sqrt(1-0.1^2))

Evaluating ... ...

M_r = 5.02518907629606

STEP 3: Convert Result to Output's Unit

5.02518907629606 --> No Conversion Required

FINAL ANSWER

5.02518907629606 ≈ 5.025189 <-- Resonant Peak

(Calculation completed in 00.004 seconds)

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< Fundamental Parameters Calculators

Angle of Asymptotes

LaTeX Go Angle of Asymptotes = ((2*(modulus(Number of Poles-Number of Zeroes)-1)+1)*pi)/(modulus(Number of Poles-Number of Zeroes))

Bandwidth Frequency given Damping Ratio

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

Closed Loop Negative Feedback Gain

LaTeX Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))

Closed Loop Gain

LaTeX Go Closed-Loop Gain = 1/Feedback Factor

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Bandwidth Frequency given Damping Ratio

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

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

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LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

< Modelling Parameters Calculators

Damping Ratio or Damping Factor

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

Damped Natural Frequency

LaTeX Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)

Resonant Frequency

LaTeX Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Resonant Peak

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

Resonant Peak Formula

LaTeX Go

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

How does resonance occur?

Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a simple pendulum). However, there are some losses from cycle to cycle, called damping.

How to Calculate Resonant Peak?

Resonant Peak calculator uses Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)) to calculate 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 calculate Resonant Peak using this online calculator? To use this online calculator for Resonant Peak, enter Damping Ratio (ζ) and hit the calculate button. Here is how the Resonant Peak calculation can be explained with given input values -> 5.025189 = 1/(2*0.1*sqrt(1-0.1^2)).

FAQ

What is Resonant Peak?

Resonant Peak formula is defined as the peak (maximum) value of the magnitude of frequency domain and is represented as M_r = 1/(2*ζ*sqrt(1-ζ^2)) or Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)). Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

How to calculate Resonant Peak?

Resonant Peak formula is defined as the peak (maximum) value of the magnitude of frequency domain is calculated using Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2)). To calculate Resonant Peak, you need Damping Ratio (ζ). With our tool, you need to enter the respective value for Damping Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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