## 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*Kspring))
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*Kspring)) --> 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
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Angle of Asymptotes
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Maximum Overshoot
Maximum Overshoot = e^(-(Damping Ratio*Damped Natural Frequency)/(sqrt(1-(Damping Ratio)^2)))
Damping Ratio or Damping Factor
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Number of Oscillations
Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)
Damped Natural Frequency
Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Rise Time given Damped Natural Frequency
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
Time Period of Oscillations
Time Period for Oscillations = (2*pi)/Damped Natural Frequency
Setting Time when Tolerance is 2 Percent
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time when Tolerance is 5 Percent
Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros
Delay Time
Delay Time = (1+(0.7*Damping Ratio))/Frequency
Peak Time
Peak Time = pi/Damped Natural Frequency
Rise Time given Delay Time
Rise Time = 1.5*Delay Time

## < 19 Fundamental Formulas Calculators

Bandwidth Frequency given Damping Ratio
Bandwidth Frequency = Frequency*(sqrt(1-(2*(Damping Ratio^2)))+sqrt((Damping Ratio^4)-(4*(Damping Ratio^2))+2))
Damping Ratio given Percentage Overshoot
Damping Ratio = -ln(Percentage Overshoot/100)/ sqrt((pi^2)+ln(Percentage Overshoot/100)^2)
Angle of Asymptotes
Angle of Asymptotes = (((2*Parameter for Root Locus)+1)*pi)/(Number of Poles-Number of Zeros)
Percentage Overshoot
Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))
Closed Loop Positive Feedback Gain
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
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
Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Gain-Bandwidth Product
Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth
Damped Natural Frequency
Damped Natural Frequency = Frequency*(sqrt(1-(Damping Ratio)^2))
Resonant Peak
Resonant Peak = 1/((2*Damping Ratio)*sqrt(1-(Damping Ratio)^2))
Resonant Frequency
Resonant Frequency = Frequency*sqrt(1-2*(Damping Ratio)^2)
Steady State Error for Type Zero System
Steady State Error = Coefficient Value/(1+Position Error Constant)
Steady State Error for Type 2 System
Steady State Error = Coefficient Value/Acceleration Error Constant
Steady State Error for Type 1 System
Steady State Error = Coefficient Value/Velocity Error Constant
Number of Asymptotes
Number of Asymptotes = Number of Poles-Number of Zeros
Transfer Function for Closed and Open Loop System
Transfer Function = Output of System/Input of System
Damping Ratio
Damping Ratio = Actual Damping/Critical Damping
Closed Loop Gain
Gain with Feedback = 1/Feedback Factor
Q-Factor
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*Kspring))

## 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 (Kspring) 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*Kspring)) 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 (Kspring). 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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