Question

Find the inverse Laplace transform for \(\frac{1}{(s+1)^2}\).

(a) te^t u(t)

(b) te^-t u(t)

(c) tu(t)

(d) e^t u(t)

The question was asked in an international level competition.

The origin of the question is Inverse Laplace Transform in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

Correct choice is (b) te^-t u(t)

Explanation: Given X(s) = \(\frac{1}{(s+1)^2}\)

x(t) = L^-1 [X(s)] = \(L^{-1} \Big[\frac{1}{(s+1)^2}\Big] = e^{-t} L^{-1} [\frac{1}{s^2}]\) = e^-t tu(t) = te^-t u(t).