Mass-spring system (not exactly homework)

[negation]

Case of a spring with a mass,m, that has been stretch beyond the equilibrium in the positive x direction.

mg + (-kx0) = 0
k = mg/x0

stretch:

F = mg+ [-k(x0+x1)] = mg-kx0-kx1
but since mg-kx0 = 0
F = 0-kx1 = ma

ma = -kx1
a = -kx1/m

How do I arrive at the corollary from a = - kx1/m to ω0 = SQRT[k/x]?

 

[NascentOxygen]

$a = -kx_1$ can be expressed as $d^2x / dt^2 = -kx_1$

Now it comes down to fitting a solution to this differential equation...