Question

The Laplace transform of the signal t^3 u(t) is _____________

(a) \(\frac{3}{s^4}\)

(b) \(\frac{-3}{s^4}\)

(c) \(\frac{6}{s^4}\)

(d) \(\frac{-6}{s^4}\)

I had been asked this question during an interview.

Enquiry is from Common Laplace Transforms in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Right choice is (c) \(\frac{6}{s^4}\)

For explanation: p (t) = t u (t)

Laplace transform of p (t), p (s) = \(\frac{1}{s^2}\)

Again, q (t) = – t p (t)

Laplace transform of q (t), q (s) = \(\frac{d}{dx}\)  P(s) = \(\frac{-2}{s^3}\)  

Again, x (t) = -t q (t)

Laplace transform of x (t), x (s) = \(\frac{6}{s^4}\).