Find the la place transform.?

Question

I need to find the la place transform for: 3/ (S^2-6S+13).

Thanks.

Answer 1

I think you are already in Laplace domain, may be the question is like this:

3/ (t^2-6t+13).

Or maybe you want the inverse Laplace transform?

Answer 2

S^2 - 6S + 13 =

S^2 - 6S + 3^2 - 9 + 13 =

(S - 3)^2 + 4

3 / (S^2 - 6S + 13) =

3 / ((S - 3)^2 + 4) =

which is near the form of

ω / ((S - α)^2 + ω^2)

Multiplying by 2/2 and rearranging, we have

(3/2)(2 / ((S - 3)^2 + 4))

which IS in the form of

k(ω / ((S - α)^2 + ω^2))

which has the inverse transform

k(e^αt)(sinωt)u(t)

Filling in the constants, we have

(3/2)(e^3t)(sin2t)u(t)