Question

The Laplace transform of signal u(t-2) is ___________

(a) \(\frac{-e^{-2s}}{s}\)

(b) \(\frac{e^{-2s}}{s}\)

(c) \(\frac{e^{-2s}}{1+s}\)

(d) Zero

This question was addressed to me by my college director while I was bunking the class.

Question is from Common Laplace Transforms topic in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

Right choice is (b) \(\frac{e^{-2s}}{s}\)

To elaborate: X(s) = \(\int_0^∞ x(t)  e^{-st} \,dt\)

Here, the given signal is u (t-2).

Hence, u (t-2) = 1 for all t>2 and =0 for all t<2.

So, limit is from 2 to ∞

∴ Laplace of signal= \(\int_2^∞ e^{-st} \,dt = \frac{e^{-2s}}{s}\).