How to Calculate and Solve for Damped Natural Frequency | Dynamic Characteristics of Instruments

Last Updated on January 20, 2021

The image above represents damped natural frequency.

To compute for damped natural frequency, two essential parameters are needed and these parameters are Undamped Natural Frequency (ω_o) and Dumping Ratio (ε).

The formula for calculating damped natural frequency:

ω_d = ω_o√(1 – ε²)

Where:

ω_d = Damped Natural Frequency
ω_o = Undamped Natural Frequency
ε = Dumping Ratio

Let’s solve an example;
Find the damped natural frequency when the undamped natural frequency is 48 and the dumping ratio is 12.

This implies that;

ω_o = Undamped Natural Frequency = 48
ε = Dumping Ratio = 12

ω_d = ω_o√(1 – ε²)
ω_d = 48 x √(1 – 12²)
ω_d = 48 x √(1 – 144)
ω_d = 48 x √(-143)
ω_d = 48 x NaN
ω_d = NaN

Therefore, the damped natural frequency is NaN.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the damped natural frequency.

To get the answer and workings of the damped natural frequeny 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

Now, Click on Dynamic Characteristics of Instruments under Instrumentation

Now, Click on Damped Natural Frequency under Dynamic Characteristics of Instruments

The screenshot below displays the page or activity to enter your values, to get the answer for the damped natural frequency according to the respective parameters which is the Undamped Natural Frequency (ω_o) and Dumping Ratio (ε).

Now, enter the values appropriately and accordingly for the parameters as required by the Undamped Natural Frequency (ω_o) is 48 and Dumping Ratio (ε) is 12.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the damped natural frequency and presents the formula, workings and steps too.