How to Calculate and Solve for Dumping Ratio | Step and Frequency Response | Dynamic Characteristics of Instruments

January 19, 2021April 23, 2024 Loveth Idoko

Last Updated on April 23, 2024

The image above represents the dumping ratio | step and frequency response. To calculate the dumping ratio | step and frequency response, three essential parameters are needed: Co-efficient (ao), Co-efficient (a1), and Co-efficient (a2).

The formula for calculating dumping ratio | step and frequency response:

ε = ^a₁ / _{2√(a_o a₂)}

Where:

ε = Dumping Ratio
a_o = Co-efficient
Also, a₁ = Co-efficient
a₂ = Co-efficient

Let’s solve an example;
Find the dumping ratio when the co-efficient is 14, the co-efficient is 7 and the co-efficient is 10.

This implies that;

a_o = Co-efficient = 14
a₁ = Co-efficient = 7
And then, a₂ = Co-efficient = 10

ε = ^a₁ / _{2√(a_o a₂)}
ε = ⁷ / _{2 x √(14 x 10)}
That is, ε = ⁷ / _{2 x √(140)}
ε = ⁷ / _{2 x 11.83}
So, ε = ⁷ / _23.66
ε = 0.295

Therefore, the dumping ratio | step frequency response is 0.295.

Calculating for the Co-efficient when the Dumping Ratio, the Co-efficient and the Co-efficient are Given

a₁ = ε x 2√(a_o . a₂)

Where;

a₁ = Co-efficient
ε = Dumping Ratio
a_o = Co-efficient
a₂ = Co-efficient

Let’s solve an example;
Find the co-efficient when the dumping ratio is 10, the co-efficient is 4 and the co-efficient is 6.

This implies that;

ε = Dumping Ratio = 10
a_o = Co-efficient = 4
a₂ = Co-efficient = 6

a₁ = ε x 2√(a_o . a₂)
a₁ = 10 x 2√(4 . 6)
So, a₁ = 10 x 2√(24)
a₁ = 10 x 2(4.89)
a₁ = 97.8

Therefore, the dumping ratio | step frequency response is 97.8

How to Calculate Dumping Ratio | Step and Frequency Response Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the dumping ratio | step frequency response.

To get the answer and workings of the dumping ratio | step frequency response using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on instrumentation under Materials and Metallurgical

Then, Click on Dynamic Characteristics of Instruments under Instrumentation

Now, Click on Dumping Ratio | Step Frequency Response under Dynamic Characteristics of Instruments

The screenshot below displays the page or activity to enter your values, to get the answer for the dumping ratio | step frequency response according to the respective parameters which is the Co-efficient (a_o), Co-efficient (a₁) and Co-efficient (a₂).

Now, enter the values appropriately and accordingly for the parameters as required by the Co-efficient (a_o) is 14, Co-efficient (a₁) is 7 and Co-efficient (a₂) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the dumping ratio | step frequency response and presents the formula, workings and steps too.