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ISRO EC 2023 Q.18: solution and answer

ISRO 2023 · ECQ.18 · 1 mark · MCQ

Transfer function H(s) = 1/(s + 3)^2 has poles

  1. (A)

    -3, 3

  2. (B)

    -3

  3. (C)

    -3, -3

  4. (D)

    3

See the question in the paper
ISRO EC 2023 question 18Tap to open full size

Answer and solution

ANSWER

The poles are at , a double pole at , which is option (c).

Official answer: CSource: ISRO's revised and final answer key of 16 February 2024

  1. The poles of are the values of at which the denominator is zero.

  2. The denominator is .

  3. Setting gives from each factor, so the poles are : a repeated (double) pole at .

  4. Option (a) is wrong: a pole at would need a factor , and there is none.

  5. Option (b) gives the right location but lists the pole only once, leaving out its multiplicity of two. Option (c) lists both poles, so it is the complete answer.

  6. Option (d) is wrong: at the denominator is , so it is not a pole.

KEY IDEA

Poles are the roots of the denominator, and a squared factor gives a repeated pole at , counted twice.

WATCH OUT FOR

Reading as giving poles at both and , or stopping at a single pole at and forgetting that the square makes it a double pole.

From the ISRO EC 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 4 ISRO Laplace questions, with notes

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