Question

The Laplace transform of the function 6e^5tcos(2t) – e^7t is ______________

(a) \(\frac{6(s-5)}{(s-5)^2+4} – \frac{1}{s-7}\)

(b) \(\frac{6(s-5)}{(s-5)^2+4} + \frac{1}{s-7}\)

(c) \(\frac{6(s+5)}{(s+5)^2+4} – \frac{1}{s-7}\)

(d) \(\frac{6(s+5)}{(s+5)^2+4} + \frac{1}{s-7}\)

I have been asked this question during an online exam.

Origin of the question is Laplace Transform of a Periodic Function in portion Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Correct option is (a) \(\frac{6(s-5)}{(s-5)^2+4} – \frac{1}{s-7}\)

Easiest explanation: L {6e^5tcos(2t) – e^7t} = \(\frac{6(s-5)}{(s-5)^2+4} – \frac{1}{s-7}\).