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

+1 vote
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

by (42.1k points)
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)} = $\frac{e^{-2s}+e^{-2s}}{s} = \frac{cosh⁡2s}{s}$.

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