# 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** (a _{2}).**

The formula for calculating undamped natural frequency:

ω_{o} = √(^{ao} / _{a2})

Where:

ω_{o} = Undamped Natural Frequency

a_{o} = Co-efficient

a_{2} = 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;

a_{o} = Co-efficient = 32

a_{2} = Co-efficient = 3

ω_{o} = √(^{ao} / _{a2})

Then, ω_{o} = √(^{32} / _{3})

ω_{o} = √(10.66)

ω_{o} = 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**

a_{o} = a_{2} x w_{o}^{2}

Where;

a_{o} = Co-efficient

ω_{o} = Undamped Natural Frequency

a_{2} = 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;

ω_{o} = Undamped Natural Frequency = 12

a_{2} = Co-efficient = 6

a_{o} = a_{2} x w_{o}^{2}

So, a_{o} = 6 x 12^{2}

a_{o} = 6 x 144

a_{o} = 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**

a_{2} = ^{ao} / _{wo2}

Where;

a_{2} = Co-efficient

ω_{o} = Undamped Natural Frequency

a_{o} = 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;

ω_{o} = Undamped Natural Frequency = 7

a_{o} = Co-efficient = 21

a_{2} = ^{ao} / _{wo2}

That is, a_{2} = ^{21} / _{72}

a_{2} = ^{21} / _{49}

a_{2} = 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 (a _{o}) **and

**Co-efficient (a**

_{2}).Now, enter the values appropriately and accordingly for the parameters as required by the **Co-efficient (a _{o})** is

**32**and

**Co-efficient (a**is

_{2})**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.