LCM of two numbers

Damping Ratio or Damping Factor Calculator

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Fundamental Parameters Second Order System

✖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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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 - 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

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 ≈ 0.188147 <-- Damping Ratio

(Calculation completed in 00.004 seconds)

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National Institute of Information Technology (NIIT), Neemrana

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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

< 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))

Damping Ratio or Damping Factor Formula

LaTeX Go

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 defined as 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 defined as 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 defined as 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 3 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)
Damping Ratio = Actual Damping/Critical Damping

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