Question

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

(a) te^-t u(t)

(b) e^-t  sin⁡t u(t)

(c) e^-t  cos⁡t u(t)

(d) e^-t u(t)

The question was asked during a job interview.

My enquiry is from Inverse Laplace Transform topic in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Correct answer is (b) e^-t  sin⁡t u(t)

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

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