Question

Find the laplace transform of the following time functions:
(a) f(t) = sin(2t) + 2cos(2t) + (e^-t)sin(2t)

(I forget how to do laplace transforms, I did it years ago)

Answer 1

i just watched a good video on this, but i have no idea how to do them. however, here is your answer
http://www.wolframalpha.com/input/?i=laplace+transform++f%28t%29+%3D+sin%282t%29+%2B+2cos%282t%29+%2B+%28e^-t%29sin%282t%29

Answer 2

and here is a fairly decent explanation of the laplace transform of sine
if i recall from the video, multiplying by e^-t is just a shift, but it is worked out here as well
http://cnyack.homestead.com/files/alaplace/lapfun1.htm

Answer 3

if you are interested and have some time, here is the video courtesy of jamesj
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/