Question

Find the inverse Laplace transformation:

Answer 1

\[\huge F(s)=\frac{ 4s+8 }{ s^2+4s+85 }\]
\[\huge \mathfrak{L}^{-1}\left\{ F(s) \right\}=??\]

I initially started by factoring out the 4 and then completing the square on the bottom, leaving me with:\[\large 4 \cdot \frac{ (s+2) }{ (s+2)^2+9^2 }\]This follows the form of \(\cos(at)\), which is\[\large \frac{ s }{ s^2+a^2 }\]
So my final answer was:\[\large 4e^{-2t} \cos(3t)\]But this was marked wrong. Can anybody see my error here?

Answer 2

Oh geez, I found my error. Yikes X)

Answer 3

Ah :D

Answer 4

I accidentally took the square root of a! Not good! Supposed to be cos(9t) X) Haha