Problem states: Find the frequency, periodic time and solution for each of the following harmonic oscillators:

(a). f''(t) +f(t)=0 given that f(0)=0 and f'=1

(b). 6f''(t)+2f'(t)+9f(t)=0 given that f(0)=0 and f'(0)=3

Okay. So I know to do the substitutions (L{f''(t)} = s^2.F(s) - sf(0) - f'(0)) but I have trouble with doing the inverse Laplace (i.e. the solution XD). I didn't get to try this because I got stuck on a similar problem and couldn't solve that one either! But this one I have to present in class I don't want to let them down!!!!

D:

I guess frequency would be equal to sqrt(b/a) radians of equation af''(t)+bf(t)=0? And would periodic time be equal to 2*pi/sqrt(b/a) or would that be the term in the unit step? Thanks for any help you can give me.