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

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Team Softusvista
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1100+ more calculators!

19 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))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive 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 Negative Feedback Gain
Go Gain with Feedback = Open Loop Gain of an OP-AMP/(1+(Feedback Factor*Open Loop Gain of an OP-AMP))
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)
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
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))
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Transfer Function for Closed and Open Loop System
Go Transfer Function = Output of System/Input of System
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Go Closed-Loop Gain = 1/Feedback Factor
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

25 Control System Design Calculators

Time Response in Overdamped Case
Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))
Time Response of Critically Damped System
Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)
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))
Rise Time given Damping Ratio
Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Time Response in Undamped Case
Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)
Peak Time given Damping Ratio
Go Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^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)))
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Resonant Frequency
Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)
Number of Oscillations
Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Time of Peak Overshoot in Second Order System
Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency
Rise Time given Damped Natural Frequency
Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Steady State Error for Type Zero System
Go Steady State Error = Coefficient Value/(1+Position of Error Constant)
Delay Time
Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
Steady State Error for Type 2 System
Go Steady State Error = Coefficient Value/Acceleration Error Constant
Time Period of Oscillations
Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Steady State Error for Type 1 System
Go Steady State Error = Coefficient Value/Velocity Error Constant
Setting Time when Tolerance is 2 Percent
Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Peak Time
Go Peak Time = pi/Damped Natural Frequency
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)
Rise Time given Delay Time
Go Rise Time = 1.5*Delay Time

12 Modelling 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))
Damping Ratio given Percentage Overshoot
Go Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt(pi^2+ln(Percentage Overshoot/100)^2)
Percentage Overshoot
Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
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)
Gain-Bandwidth Product
Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
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))
Number of Asymptotes
Go Number of Asymptotes = Number of Poles-Number of Zeroes
Damping Ratio given Critical Damping
Go Damping Ratio = Actual Damping/Critical Damping
Q-Factor
Go Q Factor = 1/(2*Damping Ratio)

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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!