Question

The Laplace transform of the function e^-2tcos(3t) + 5e^-2tsin(3t) is ____________

(a) \(\frac{(s+2)-15}{(s+2)^2-9}\)

(b) \(\frac{(s+2)+15}{(s+2)^2-9}\)

(c) \(\frac{(s+2)+15}{(s+2)^2+9}\)

(d) \(\frac{(s+2)-15}{(s+2)^2+9}\)

The question was asked during an online interview.

Asked question is from Laplace Transform of a Periodic Function topic in section Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Correct option is (c) \(\frac{(s+2)+15}{(s+2)^2+9}\)

For explanation I would say: L {e^-2tcos(3t) + 5e^-2tsin(3t)} =  \(\frac{(s+2)}{(s+2)^2+9} + \frac{5 3}{(s+2)^2+9}\)

= \(\frac{(s+2)+15}{(s+2)^2+9}\).