Differential equation using laplace

[seang]

Homework Statement

How do I solve the following differential equation with the Laplace Transform:?
f(t)'' - a*f(t) = 0 (all ICs are equal to zero).

Homework Equations

The Attempt at a Solution

So, I get something like F(s)*(s^2 - a) = 0. I don't know where to go from there.

 

[Dick]

Your equation is missing terms which correspond to the boundary behavior of f(t). F(s)=0 is not the only solution.

 

[Dick]

Hmmm. If as you say all IC's are 0. f(0)=f'(0)=0. Then f(t)=0 is the only solution. Pretty trivial use of laplace transforms.