Question

laplace sinat

Answer 1

help pls

Answer 2

Do you know how to do Laplace transforms, or are you just having trouble with this one in particular?

Answer 3

yes

Answer 4

\[ \mathcal{L} ( \sin (at) ) = \int_{0}^{\infty}e^{-st} \sin(at) dt \] Can you do the indefinite integral?

Answer 5

no
continue

Answer 6

Well, I don't remember how it is done, and it's time for me to go to sleep. But you end up with \[-\frac{e^{-st}(a \cos(at) + s \sin(at)}{a^2+s^2}\] which you evaluate at t = infinity and t = 0 and subtract the latter from the former. The former goes to 0 as t -> infinity thanks to the e^{-st} term, so it is
\[0 - (-\frac{e^{s*0}(a \cos(a*0) + s \sin(a*0))}{a^2 + s^2}) = \frac{1(a\cos(0) + s\sin(0))}{a^2+s^2}=\frac{a}{a^2+s^2}\]