Question

Find the Laplace transform of x(t) = u(t+2) + u(t-2).

(a) \(\frac{cos⁡2s}{s}\)

(b) \(\frac{cosh⁡2s}{s}\)

(c) \(\frac{sinh⁡2s}{s}\)

(d) \(\frac{sin⁡2s}{s}\)

I have been asked this question in quiz.

This key question is from Properties of the Laplace Transform in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

The correct answer is (b) \(\frac{cosh⁡2s}{s}\)

Best explanation: Given x(t) = u(t+2) + u(t-2)

We know that the Laplace transform u(t) ↔ \(\frac{1}{s}\)

Time shifting property states that L{x(t±t0)} = X(s)e^±st0

L{u(t-2)}=\(e^{\frac{-2s}{s}}\); L{u(t+2)}=\(e^{\frac{2s}{s}}\)

∴X(s) = L{u(t+2)+u(t-2)} = \(\frac{e^{-2s}+e^{-2s}}{s} = \frac{cosh⁡2s}{s}\).