Question

Find the \(L^{-1} (\frac{1}{(s+2)^4})\).

(a) \(e^{-2t}×3\)

(b) ⁡\(e^{-2t}×\frac{t^3}{3}\)

(c) \(e^{-2t}×\frac{t^3}{6}\)

(d) \(e^{-2t}×\frac{t^2}{6}\)

I had been asked this question in an interview for job.

Origin of the question is General Properties of Inverse Laplace Transform in section Laplace Transform of Engineering Mathematics

Answer 1

The correct option is (c) \(e^{-2t}×\frac{t^3}{6}\)

The best I can explain: In the given question,

\(L^{-1} (\frac{1}{(s+2)^4})=e^{-2t} L^{-1} \frac{1}{s^4}\) —————– By the first shifting property

=\(e^{-2t}×\frac{t^3}{3!}\)

=\(e^{-2t}×\frac{t^3}{6}\).