How to Calculate and Solve for Transfer Function (Sensitivity) | Second Order Instruments | Dynamic Characteristics of Instruments

The image above represents transfer function (sensitivity). To calculate transfer function (sensitivity) | Second Order Instrument, five essential parameters are needed and these parameters are Static Sensitivity (k), Dumping Ratio (ε), Undefined Natural Frequency (ω_o), Differentiation Value (^d / _dt) (D) and Differentiation Value (^d2 / _dt²) (D²).

The formula for calculating transfer function (sensitivity):

c = ^k / _{1 + ^2εD / ωo + ^D2 / ωo²}

Where:

c = Sensitivity
k = Static Sensitivity
ε = Dumping Ratio
ω_o = Undefined Natural Frequency
D = Differential Value
D² = Differential Value

Let’s solve an example;
Find the transfer function when the static sensitivity is 8, the dumping ratio is 12, the undefined natural frequency is 10, the differential value is 7 and the differential value is 3.

This implies that;

k = Static Sensitivity = 8
ε = Dumping Ratio = 12
ω_o = Undefined Natural Frequency = 10
D = Differential Value = 7
D² = Differential Value = 3

c = ^k / _{1 + ^2εD / ωo + ^D2 / ωo²}
Then, c = ⁸ / _{1 + ^{2 x 12 x 7} / 10 + ³ / 10²}
c = ⁸ / _{1 + ¹⁶⁸ / 10 + ³ / 100}
c = ⁸ / _{1 + 16.8 + 0.03}
So, c = ⁸ / _17.830
c = 0.448

Therefore, the transfer function (sensitivity) is 0.448.

Read more: How to Calculate and Solve for Time Constant | Second Order Instruments | Dynamic Characteristics of Instruments

How to Calculate Transfer Function (Sensitivity) | Second Order Instruments With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the transfer function (sensitivity) | second Order Instrument.

To get the answer and workings of the transfer function (sensitivity) | second Order Instrument 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

Then, Click on Transfer Function (sensitivity)| Second Order Instrument under Dynamic Characteristics of Instruments

The screenshot below displays the page or activity to enter your values, to get the answer for the transfer function (sensitivity) | second Order Instrument according to the respective parameters which is the Static Sensitivity (k), Dumping Ratio (ε), Undefined Natural Frequency (ω_o), Differentiation Value (^d / _dt) (D) and Differentiation Value (^d2 / _dt²) (D²).

Now, enter the values appropriately and accordingly for the parameters as required by the Static Sensitivity (k) is 8, Dumping Ratio (ε) is 12, Undefined Natural Frequency (ω_o) is 10, Differentiation Value (^d / _dt) (D) is 7 and Differentiation Value (^d2 / _dt²) (D²) is 3.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the transfer function (sensitivity) | second Order Instrument and presents the formula, workings and steps too.