Question

If u (t) = 1 for t >= 0 and u (t) = 0 for t < 0, determine the Laplace transform of [u (t) – u (t – a)].

(a) 1/s(1+e^(-as))

(b) 1/s(1-e^(-as))

(c) 1/s(1+e^as)

(d) 1/s(1-e^as)

I have been asked this question by my college director while I was bunking the class.

My doubt stems from Operational Transforms in portion Intoduction to the Laplace Transform of Network Theory

Answer 1

The correct answer is (b) 1/s(1-e^(-as))

To explain I would say: As u (t) = 1 for t >= 0 and u (t) = 0 for t < 0, the Laplace transform of [u (t) – u (t – a)] is L[u (t)– u (t – a)] = 1/s-e^(-as)1/s = 1/s (1-e^(-as)).