building a laplace transform

Question

F(s) is the laplace transform of the function (f(t))

Numerator is equal to 1 and the denominator is a 2nd degree polynomial with complex conjugate roots of my choice (both s and w are non zero in s +/- jw).

Build F(s) and find f(t).

How would I go on about doing this? On paper and solving it in MATLAB to find the partial fraction expansion? As well as finding the inverse of it? Both answers have to be the same. I tried doing it but I'm unsure on how to "build" a function.

Thanks

Answer 1

I'm understanding that $f(s)=\frac{1}{As^2+w^2}$, with $A,w$ real constants. Well, this would be my roadmap:

1. Write $f(s)$ as the sum of two fractions
2. Use the linearity of the Laplace transform
3. Compute the inverse transform of each simple fraction (should be a familiar type)
4. Put together the pieces