Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
570 views
in Electronics by (240k points)
closed by

What is the value of ωn in the given transfer function?

\(G\left( s \right) = \frac{{36}}{{{s^2} + 4.2s + 36}}\)


1. 72
2. 4.2
3. 36
4. 6

1 Answer

0 votes
by (238k points)
selected by
 
Best answer
Correct Answer - Option 4 : 6

Concept:

The transfer function of the standard second-order system is:

\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\)

ζ is the damping ratio

ωn is the natural frequency

Characteristic equation: \({s^2} + 2\zeta {\omega _n} + \omega _n^2\)

Roots of the characteristic equation are: \( - \zeta {\omega _n} + j{\omega _n}\sqrt {1 - {\zeta ^2}} = - \alpha \pm j{\omega _d}\)

α is the damping factor

Calculation:

Transfer function \(G\left( s \right) = \frac{{36}}{{{s^2} + 4.2s + 36}}\)

By comparing the above transfer function with the standard second-order system,

\(\omega _n^2 = 36 \Rightarrow {\omega _n} = 6\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...