Question

laplace transformation of{ Sinat Sinbt}?​

Answer 1

Answer:

Given f(t)=sin(at) I want to calculate the Laplace transform of f(t).

I have determined by using integration by parts twice, that the answer should be

F(s)=as2+a2

Now I want to recalculate it by using just that

sin(at)=12i(eati−e−ati)

So the integral becomes

12i∫∞0e−st(eati−e−ati)=

12i∫∞0et(ai−s)−e−t(ai+s)dt=

12i[1ai−set(ai−s)]∞0+12i[1ai+se−t(ai+s)]∞0

My question now is: How to determine the limit of et(ai−s) as t goes to ∞ ?

Answer 2

Answer:

2abs/[s^2+(a+b)^2][s^2(a-b)^2]