What's the inverse Laplace transform of this?

[AdrianZ]

Homework Statement

$$L^{-1}\{\frac{1}{(s^2+4)^2}\}$$

Homework Equations

The Attempt at a Solution

I have no idea how to solve this. Any idea to being solving the problem would be appreciated.

 

[gomunkul51]

One way so solve it (propably not the simplest but an interesting one) would be to use the fact that F(s)G(s) (multiplication of the functions) in Laplace plane is f(t)*g(t) (convolution of the functions) in "time" plane.

$$<br /> L^{-1}\left \{ \frac{1}{(s^2+4)^{2}} \right \} = L^{-1}\left \{ \frac{1}{(s^2+4)} \right \}*L^{-1}\left \{ \frac{1}{(s^2+4)} \right \}<br />$$ROM.