Bandwidth Frequency given Damping Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))
fb = ωn*(sqrt(1-(2*ζ^2))+sqrt(ζ^4-(4*ζ^2)+2))
This formula uses 1 Functions, 3 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
Bandwidth Frequency - (Measured in Hertz) - Bandwidth Frequency is the range of frequencies over which, the magnitude of frequency domain drops to 70.7% from its zero frequency value.
Natural Frequency of Oscillation - (Measured in Hertz) - The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.
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
Natural Frequency of Oscillation: 23 Hertz --> 23 Hertz No Conversion Required
Damping Ratio: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
fb = ωn*(sqrt(1-(2*ζ^2))+sqrt(ζ^4-(4*ζ^2)+2)) --> 23*(sqrt(1-(2*0.1^2))+sqrt(0.1^4-(4*0.1^2)+2))
Evaluating ... ...
fb = 54.9696597723011
STEP 3: Convert Result to Output's Unit
54.9696597723011 Hertz --> No Conversion Required
FINAL ANSWER
54.9696597723011 54.96966 Hertz <-- Bandwidth Frequency
(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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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

Second Order System Calculators

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

Control System Design Calculators

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)))
Delay Time
​ 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))

Bandwidth Frequency given Damping Ratio Formula

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

What is bandwidth?

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth.

How to Calculate Bandwidth Frequency given Damping Ratio?

Bandwidth Frequency given Damping Ratio calculator uses Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2)) to calculate the Bandwidth Frequency, Bandwidth Frequency given Damping Ratio is defined as the frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance. Bandwidth Frequency is denoted by fb symbol.

How to calculate Bandwidth Frequency given Damping Ratio using this online calculator? To use this online calculator for Bandwidth Frequency given Damping Ratio, enter Natural Frequency of Oscillation n) & Damping Ratio (ζ) and hit the calculate button. Here is how the Bandwidth Frequency given Damping Ratio calculation can be explained with given input values -> 54.96966 = 23*(sqrt(1-(2*0.1^2))+sqrt(0.1^4-(4*0.1^2)+2)).

FAQ

What is Bandwidth Frequency given Damping Ratio?
Bandwidth Frequency given Damping Ratio is defined as the frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance and is represented as fb = ωn*(sqrt(1-(2*ζ^2))+sqrt(ζ^4-(4*ζ^2)+2)) or Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2)). The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position & Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
How to calculate Bandwidth Frequency given Damping Ratio?
Bandwidth Frequency given Damping Ratio is defined as the frequency value at which output drops by 3 dB of maximum response value, or reduces to (1/√2) of value at resonance is calculated using Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2)). To calculate Bandwidth Frequency given Damping Ratio, you need Natural Frequency of Oscillation n) & Damping Ratio (ζ). With our tool, you need to enter the respective value for Natural Frequency of Oscillation & 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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