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GATE 2014 EC (EC4) – Question 38

Networks, Signals and Systems · Continuous-time Signals · 2 marks · Multiple choice

f(t) has unilateral Laplace transform $1/(s^2+s+1)$. Find the unilateral transform of g(t) = tf(t).

  1. $-s/(s^2+s+1)^2$
  2. $-(2s+1)/(s^2+s+1)^2$
  3. $s/(s^2+s+1)^2$
  4. $(2s+1)/(s^2+s+1)^2$

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Correct answer: (D) $(2s+1)/(s^2+s+1)^2$

Explanation

The time-multiplication property is L{tf(t)}=−dF(s)/ds. With F(s)=1/(s²+s+1), differentiating and negating gives **(2s+1)/(s²+s+1)²,D**. The minus sign in the transform property cancels the derivative’s minus sign.