1.

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»

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)).



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