FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Damping Ratio or Damping Factor Formula

GoDamping Ratio given Critical Damping Formula

GoDamping Ratio given Percentage Overshoot Formula

Fx Copy

LaTeX Copy

Damping Ratio in control system is defined as the ratio with which any signal gets decayed. Check FAQs

ζ = \frac{c}{2 \cdot \sqrt{m \cdot K spring}}

ζ - Damping Ratio?c - Damping Coefficient?m - Mass?K_spring - Spring Constant?

Damping Ratio or Damping Factor Example

With values

With units

Only example

Here is how the Damping Ratio or Damping Factor equation looks like with Values.

Here is how the Damping Ratio or Damping Factor equation looks like with Units.

Here is how the Damping Ratio or Damping Factor equation looks like.

0.1881 = \frac{16}{2 \cdot \sqrt{35.45 \cdot 51}}

0.1881 = \frac{16}{2 \cdot \sqrt{35.45kg \cdot 51N/m}}

0.1881 = \frac{16}{2 \cdot \sqrt{35.45 \cdot 51}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Electronics » Category

Control System » fx Damping Ratio or Damping Factor

Damping Ratio or Damping Factor Solution

Follow our step by step solution on how to calculate Damping Ratio or Damping Factor?

FIRST Step Consider the formula

ζ = \frac{c}{2 \cdot \sqrt{m \cdot K spring}}

Next Step Substitute values of Variables

∴

ζ = \frac{16}{2 \cdot \sqrt{35.45kg \cdot 51N/m}}

Next Step Prepare to Evaluate

∴

ζ = \frac{16}{2 \cdot \sqrt{35.45 \cdot 51}}

Next Step Evaluate

∴

ζ = 0.188146775281754

LAST Step Rounding Answer

∴

ζ = 0.1881

Damping Ratio or Damping Factor Formula Elements

Variables

Functions

Damping Ratio

Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Ratio

Damping Coefficient

Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

Symbol: c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Mass

Mass is defined as the force exerted by an object due the effect of gravity on any surface.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass

Spring Constant

Spring Constant is the displacement of the spring from its equilibrium position.

Symbol: K_spring

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Spring Constant

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.

Syntax: sqrt(Number)

Other Formulas to find Damping Ratio

Go Damping Ratio given Critical Damping

ζ = \frac{C}{C c}

Go Damping Ratio given Percentage Overshoot

ζ = - \frac{\ln (\frac{% o}{100})}{\sqrt{π^{2} + {\ln (\frac{% o}{100})}^{2}}}

Other formulas in Fundamental Parameters category

Go Damped Natural Frequency

ω d = ω n \cdot \sqrt{1 - ζ^{2}}

Go Resonant Peak

M r = \frac{1}{2 \cdot ζ \cdot \sqrt{1 - ζ^{2}}}

Go Resonant Frequency

ω r = ω n \cdot \sqrt{1 - 2 \cdot ζ^{2}}

Go Bandwidth Frequency given Damping Ratio

f b = ω n \cdot (\sqrt{1 - (2 \cdot ζ^{2})} + \sqrt{ζ^{4} - (4 \cdot ζ^{2}) + 2})

How to Evaluate Damping Ratio or Damping Factor?

Damping Ratio or Damping Factor evaluator uses Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)) to evaluate 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 evaluate Damping Ratio or Damping Factor using this online evaluator? To use this online evaluator for Damping Ratio or Damping Factor, enter Damping Coefficient (c), Mass (m) & Spring Constant (K_spring) and hit the calculate button.

FAQs on Damping Ratio or Damping Factor

What is the formula to find Damping Ratio or Damping Factor?

The formula of Damping Ratio or Damping Factor is expressed as Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). Here is an example- 0.188147 = 16/(2*sqrt(35.45*51)).

How to calculate Damping Ratio or Damping Factor?

With Damping Coefficient (c), Mass (m) & Spring Constant (K_spring) we can find Damping Ratio or Damping Factor using the formula - Damping Ratio = Damping Coefficient/(2*sqrt(Mass*Spring Constant)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Damping Ratio?

Here are the different ways to Calculate Damping Ratio-

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

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Damping Ratio or Damping Factor Formula

​GoDamping Ratio given Critical Damping Formula

​GoDamping Ratio given Percentage Overshoot Formula

Damping Ratio or Damping Factor Example

Damping Ratio or Damping Factor Solution

Damping Ratio or Damping Factor Formula Elements

Other Formulas to find Damping Ratio

Other formulas in Fundamental Parameters category

How to Evaluate Damping Ratio or Damping Factor?

FAQs on Damping Ratio or Damping Factor

Variable Name

GoDamping Ratio given Critical Damping Formula

GoDamping Ratio given Percentage Overshoot Formula