How to Calculate and Solve for Undamped Natural Frequency | Dynamic Characteristics of Instruments
Last Updated on April 23, 2024
The image above represents undamped natural frequency. Two essential parameters are needed to calculate undamped natural frequency: co-efficient (ao) and co-efficient (a2).
The formula for calculating undamped natural frequency:
ωo = √(ao / a2)
Where:
ωo = Undamped Natural Frequency
ao = Co-efficient
a2 = Co-efficient
Let’s solve an example;
Find the undamped natural frequency when the co-efficient is 32 and the co-efficient is 3.
This implies that;
ao = Co-efficient = 32
a2 = Co-efficient = 3
ωo = √(ao / a2)
Then, ωo = √(32 / 3)
ωo = √(10.66)
ωo = 3.265
Therefore, the undamped natural frequency is 3.265.
Calculating for the Co-efficient when the Undamped Natural Frequency and the Co-efficient are Given
ao = a2 x wo2
Where;
ao = Co-efficient
ωo = Undamped Natural Frequency
a2 = Co-efficient
Let’s solve an example;
Find the co-efficient when the undamped natural frequency is 12 and the co-efficient is 6.
This implies that;
ωo = Undamped Natural Frequency = 12
a2 = Co-efficient = 6
ao = a2 x wo2
So, ao = 6 x 122
ao = 6 x 144
ao = 864
Therefore, the co-efficient is 864.
Read more: How to Calculate and Solve for Damped Natural Frequency | Dynamic Characteristics of Instruments
Calculating for the Co-efficient when the Undamped Natural Frequency and the Co-efficient are Given
a2 = ao / wo2
Where;
a2 = Co-efficient
ωo = Undamped Natural Frequency
ao = Co-efficient
Let’s solve an example;
Find the co-efficient when the undamped natural frequency is 7 and the co-efficient is 21.
This implies that;
ωo = Undamped Natural Frequency = 7
ao = Co-efficient = 21
a2 = ao / wo2
That is, a2 = 21 / 72
a2 = 21 / 49
a2 = 0.428
Therefore, the co-efficient is 0.428.
How to Calculate Undamped Natural Frequency With Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the undamped natural frequency.
To get the answer and workings of the undamped natural frequency 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
So, Click on Undamped 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 undamped natural frequency according to the respective parameters which is the Co-efficient (ao) and Co-efficient (a2).
Now, enter the values appropriately and accordingly for the parameters as required by the Co-efficient (ao) is 32 and Co-efficient (a2) is 3.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the undamped natural frequency and presents the formula, workings and steps too.
