Damping Ratio or Damping Factor Calculator

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✖Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.ⓘ Damping Coefficient [c]			+10% -10%
✖Mass is defined as the force exerted by an object due the effect of gravity on any surface.ⓘ Mass [M]			+10% -10%
✖Spring Constant is the displacement of the spring from its equilibrium position.ⓘ Spring Constant [K_spring]			+10% -10%

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

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Formula

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Damping Ratio or Damping Factor

Formula

`"ζ" = "c"/(2*sqrt("M"*"K"_{"spring"}))`

Example

`"0.188147"="16"/(2*sqrt("35.45kg"*"51N/m"))`

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Damping Ratio or Damping Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
ζ = c/(2*sqrt(M*K_spring))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - Squre root function, sqrt(Number)

Variables Used

Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Damping Coefficient - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Mass - (Measured in Kilogram) - Mass is defined as the force exerted by an object due the effect of gravity on any surface.
Spring Constant - (Measured in Newton per Meter) - Spring Constant is the displacement of the spring from its equilibrium position.

STEP 1: Convert Input(s) to Base Unit

Damping Coefficient: 16 --> No Conversion Required
Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Spring Constant: 51 Newton per Meter --> 51 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ = c/(2*sqrt(M*K_spring)) --> 16/(2*sqrt(35.45*51))

Evaluating ... ...

ζ = 0.188146775281754

STEP 3: Convert Result to Output's Unit

0.188146775281754 --> No Conversion Required

FINAL ANSWER

0.188146775281754 <-- Damping Ratio

(Calculation completed in 00.000 seconds)

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Credits

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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< 16 Control Systems Calculators

Bandwidth Frequency given Damping Ratio

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

Angle of Asymptotes

Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)

Maximum Overshoot

Go Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))

Damping Ratio or Damping Factor

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

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Damped Natural Frequency

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

Resonant Peak

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

Resonant Frequency

Go Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

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 Zeros

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Frequency

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 19 Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Frequency*(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)

Angle of Asymptotes

Go Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Closed Loop Positive Feedback Gain

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

Closed Loop Negative Feedback Gain

Go Closed-Loop Gain = 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))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Damped Natural Frequency

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

Resonant Peak

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

Resonant Frequency

Go Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position 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 Zeros

Transfer Function for Closed and Open Loop System

Go Transfer Function = Output of System/Input of System

Damping Ratio

Go Damping Ratio = Actual Damping/Critical Damping

Closed Loop Gain

Go Gain with Feedback = 1/Feedback Factor

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Damping Ratio or Damping Factor Formula

Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
ζ = c/(2*sqrt(M*K_spring))

How is damping ratio used?

To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping required to reach critical damping. The formula for the damping ratio is used for the mass-spring-damper model.

How is damping factor obtained?

The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient. The damping ratio is dimensionless, being the ratio of two coefficients of identical units.

How to Calculate Damping Ratio or Damping Factor?

Damping Ratio or Damping Factor calculator uses Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) to calculate the Damping Ratio, Damping Ratio or Damping Factor is a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. Damping Ratio is denoted by ζ symbol.

How to calculate Damping Ratio or Damping Factor using this online calculator? To use this online calculator for Damping Ratio or Damping Factor, enter Damping Coefficient (c), Mass (M) & Spring Constant (K_spring) and hit the calculate button. Here is how the Damping Ratio or Damping Factor calculation can be explained with given input values -> 0.188147 = 16/(2*sqrt(35.45*51)).

FAQ

What is Damping Ratio or Damping Factor?

Damping Ratio or Damping Factor is a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator and is represented as ζ = c/(2*sqrt(M*K_spring)) or Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system, Mass is defined as the force exerted by an object due the effect of gravity on any surface & Spring Constant is the displacement of the spring from its equilibrium position.

How to calculate Damping Ratio or Damping Factor?

Damping Ratio or Damping Factor is a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator is calculated using Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). To calculate Damping Ratio or Damping Factor, you need Damping Coefficient (c), Mass (M) & Spring Constant (K_spring). With our tool, you need to enter the respective value for Damping Coefficient, Mass & Spring Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Damping Ratio?

In this formula, Damping Ratio uses Damping Coefficient, Mass & Spring Constant. We can use 2 other way(s) to calculate the same, which is/are as follows -

Damping Ratio = Actual Damping/Critical Damping
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt((pi^2)+ln(Percentage Overshoot/100)^2)

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