FormulaDen.com

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

Damping Ratio given Percentage Overshoot Formula

GoDamping Ratio or Damping Factor Formula

GoDamping Ratio given Critical Damping 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{\ln (\frac{% o}{100})}{\sqrt{π^{2} + {\ln (\frac{% o}{100})}^{2}}}

ζ - Damping Ratio?%_o - Percentage Overshoot?π - Archimedes' constant?

Damping Ratio given Percentage Overshoot Example

With values

With units

Only example

Here is how the Damping Ratio given Percentage Overshoot equation looks like with Values.

Here is how the Damping Ratio given Percentage Overshoot equation looks like with Units.

Here is how the Damping Ratio given Percentage Overshoot equation looks like.

0.1001 = - \frac{\ln (\frac{72.9}{100})}{\sqrt{{3.1416}^{2} + {\ln (\frac{72.9}{100})}^{2}}}

0.1001 = - \frac{\ln (\frac{72.9}{100})}{\sqrt{{3.1416}^{2} + {\ln (\frac{72.9}{100})}^{2}}}

0.1001 = - \frac{\ln (\frac{72.9}{100})}{\sqrt{{3.1416}^{2} + {\ln (\frac{72.9}{100})}^{2}}}

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 given Percentage Overshoot

Damping Ratio given Percentage Overshoot Solution

Follow our step by step solution on how to calculate Damping Ratio given Percentage Overshoot?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ζ = - \frac{\ln (\frac{72.9}{100})}{\sqrt{π^{2} + {\ln (\frac{72.9}{100})}^{2}}}

Next Step Substitute values of Constants

∴

ζ = - \frac{\ln (\frac{72.9}{100})}{\sqrt{{3.1416}^{2} + {\ln (\frac{72.9}{100})}^{2}}}

Next Step Prepare to Evaluate

∴

ζ = - \frac{\ln (\frac{72.9}{100})}{\sqrt{{3.1416}^{2} + {\ln (\frac{72.9}{100})}^{2}}}

Next Step Evaluate

∴

ζ = 0.100106480562248

LAST Step Rounding Answer

∴

ζ = 0.1001

Damping Ratio given Percentage Overshoot Formula Elements

Variables

Constants

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

Percentage Overshoot

Percentage Overshoot refers to an output exceeding its final, steady-state value.

Symbol: %_o

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Percentage Overshoot

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

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 or Damping Factor

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

Go Damping Ratio given Critical Damping

ζ = \frac{C}{C c}

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 given Percentage Overshoot?

Damping Ratio given Percentage Overshoot evaluator uses Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2) to evaluate the Damping Ratio, The Damping Ratio given Percentage Overshoot formula 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 evaluate Damping Ratio given Percentage Overshoot using this online evaluator? To use this online evaluator for Damping Ratio given Percentage Overshoot, enter Percentage Overshoot (%_o) and hit the calculate button.

FAQs on Damping Ratio given Percentage Overshoot

What is the formula to find Damping Ratio given Percentage Overshoot?

The formula of Damping Ratio given Percentage Overshoot is expressed as Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2). Here is an example- 0.100106 = -ln(72.9/100)/sqrt(pi^2+ln(72.9/100)^2).

How to calculate Damping Ratio given Percentage Overshoot?

With Percentage Overshoot (%_o) we can find Damping Ratio given Percentage Overshoot using the formula - Damping Ratio = -ln(Percentage Overshoot/100)/sqrt(pi^2+ln(Percentage Overshoot/100)^2). This formula also uses Archimedes' constant and , Natural Logarithm (ln), 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=Damping Coefficient/(2*sqrt(Mass*Spring Constant))
Damping Ratio=Actual Damping/Critical Damping

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit