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Match List I with List II:

List I

(Effeet of ξ)

List II

(Condition of System)
(A) 0 < ξ < 1 (I) Over damped
(B) ξ > 1 (II) Undamped
(C) ξ = 0 (III) Unstable
(D) ξ = −1 (IV) Under damped


Choose the correct answer from the options given below:

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UGC NET Paper 2: Electronic Science 29 Oct 2022 Shift 1
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  1. (A) - (III), (B) - (I), (C) - (II), (D) - (IV)
  2. (A) - (IV), (B) - (II), (C) - (I), (D) - (III)
  3. (A) - (IV), (B) - (I), (C) - (III), (D) - (II)
  4. (A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Answer (Detailed Solution Below)

Option 4 : (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
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Detailed Solution

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System

Damping ratio

Roots of the Characteristic equation

Root in the ‘S’ plane

Undamped

ξ =0

ξ = 0 Imaginary s = ±jω­n

 

F1 U.B Madhu 2.12.19 D20

Underdamped (Practical system)

0 ≤ ξ ≤ 1

\(- \xi {\omega _n} ± j{\omega _n}\sqrt {1 - {\xi ^2}} \)

Complex Conjugate

 

F1 U.B Madhu 2.12.19 D21

Critically damped

ξ = 1

-ωn Real and equal

 

F1 U.B Madhu 2.12.19 D22

Overdamped

ξ > 1

\(- \xi {\omega _n} \mp j{\omega _n}\sqrt {{\xi ^2} - 1} \)

Real and unequal

 

F1 U.B Madhu 2.12.19 D23

 
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