Question

Find the inverse lapace of \(\frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]}\).

(a) ^1⁄3 e^t [Cos(t) – Cos(2t)].

(b) ^1⁄3 e^-t [Cos(t) + Cos(2t)].

(c) ^1⁄3 e^t [Cos(t) + Cos(2t)].

(d) ^1⁄3 e^-t [Cos(t) – Cos(2t)].

The question was asked during an interview for a job.

I'm obligated to ask this question of Laplace Transform by Properties topic in section Laplace Transform of Engineering Mathematics

Answer 1

Correct choice is (d) ^1⁄3 e^-t [Cos(t) – Cos(2t)].

Easiest explanation: Given, \(Y(s)=\frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]}\)

=\(\frac{s+1}{3(s^2+ 2*s + 2)}-\frac{s+1}{3(s^2+ 2*s + 5)}\)

=\(\frac{s+1}{3[(s+1)^2+1]}-\frac{s+1}{3[(s+1^2+4)]}\)

=\(\frac{1}{3} [e^{-t} Cos(t)]-\frac{1}{3}[e^{-t} Cos(2t)]\)

=\(\frac{1}{3} e^{-t} [Cos(t)-Cos(2t)]\)