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
303 views
in Electronics by (98.5k points)
closed by
In general which of the following system is preferred?
1. Under-damped
2. Over-damped
3. Undamped
4. Critically damped

1 Answer

0 votes
by (95.6k points)
selected by
 
Best answer
Correct Answer - Option 1 : Under-damped

Underdamped systems are the most practical and most commonly used. An underdamped system ensure the system always reaches the desired end state with some overshoot. Even though there is overshoot the damping eventually brings the system to the desired state.

Critically damped systems, are not possible to achieve in the real world and that is why they are not used.

An overdamped system would never allow the system to reach the desired end state since it is overdamped and that is why they are never used.

Important Points:

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

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

Where,

ζ is the damping ratio

ωn is the undamped natural frequency

Characteristic equation: \({s^2} + 2\zeta {\omega _n} + \omega _n^2 = 0\)

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

    The nature of the system is described by its ‘ζ’ value

    ζ

    Nature

    ζ = 0

    Undamped

    0 < ζ < 1

    Underdamped

    ζ = 1

    Critically damped

    ζ > 1

    Overdamped

    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

    ...