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 - Squre root function, 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
5.02518907629606 <-- Resonant Peak
(Calculation completed in 00.001 seconds)
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< 10+ Control Systems Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)) Go
Angle of asymptotes
Angle of Asymptotes = ((2*Parameter for Root Locus+1)*pi)/(Number of Poles-Number of Zeros) Go
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped natural frequency)/(sqrt(1-(Damping Ratio)^2))) Go
Damping ratio or Damping factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) Go
Number of oscillations
Number of Oscillations = (Setting Time*Damped natural frequency)/(2*pi) Go
Damped natural frequency
Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2)) Go
Resonant frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2) Go
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros Go
Delay time
Delay Time = (1+(0.7*Damping Ratio))/Frequency Go
Peak time
Peak Time = pi/Damped natural frequency Go

< 10+ Basics of Control System Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*((sqrt(1-(2*(Damping Ratio^2))))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2)) Go
Angle of asymptotes
Angle of Asymptotes = ((2*Parameter for Root Locus+1)*pi)/(Number of Poles-Number of Zeros) Go
Damping ratio or Damping factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) Go
Gain-bandwidth product
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid-band)*Amplifier Bandwidth Go
Damped natural frequency
Damped natural frequency = Frequency*(sqrt(1-(Damping Ratio)^2)) Go
Resonant peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2)) Go
Resonant frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2) Go
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros Go
Transfer Function for Closed and Open Loop System
Transfer Function = Output of system/Input of System Go
Closed-loop gain
Gain-with-feedback = 1/Feedback Factor Go

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 is 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 is 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 is 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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