1. ## simple laplace transforms?

Im just going over these again and was wondering if somebody could help to tell me if im doing them right please.

Q. f(t) = 2sin 3t + 4sinh 3t

A. 2 (a/s^2+a^2) + 4 (a/s^2-a^2)
2 (3/s^2+3^2) + 4 (3/s^2-3^2)
6/s^2+9 + 12/s^2-9

Q. f(t) = e^3t/2 - 6sin(2t)

A. Im not sure how to do transform the e^3t/2, im not sure which function this represents, is it e^at = 1/s-a, and where do this /2 come into it

-6sin(2t) = 12/s^2+4

2. The first one is correct.

$\mathcal{L} \{e^{\frac{3t}{2}} \} = \frac {1}{s- \frac{3}{2}}= \frac{2}{2s-3}$