Resonant Peak Solution

STEP 0: Pre-Calculation Summary
Formula Used
Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))
Mr = 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 Mr.
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
Mr = 1/(2*ζ*sqrt(1-ζ^2)) --> 1/(2*0.1*sqrt(1-0.1^2))
Evaluating ... ...
Mr = 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)

Credits

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Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
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Verified by Team Softusvista
Softusvista Office (Pune), India
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Fundamental Parameters Calculators

Angle of Asymptotes
​ 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
​ 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
​ Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
Closed Loop Gain
​ Go Closed-Loop Gain = 1/Feedback Factor

Control System Design Calculators

Bandwidth Frequency given Damping Ratio
​ 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
​ Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))
First Peak Overshoot
​ Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))
Delay Time
​ Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Modelling Parameters Calculators

Damping Ratio or Damping Factor
​ Go Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damped Natural Frequency
​ Go Damped Natural Frequency = Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)
Resonant Frequency
​ Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Resonant Peak
​ Go Resonant Peak = 1/(2*Damping Ratio*sqrt(1-Damping Ratio^2))

Resonant Peak Formula

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