How to Derive Potential Energy for SHM in Terms of Frequency?

[Mattofix]

Homework Statement

I have been asked to show that a particle of mass m executing simple harmonic motion with frequency f, has a potential energy

V(x) = 2$$\pi^{2}$$f$$^{2}$$mx$$^{2}$$

Homework Equations

The Attempt at a Solution

I know that V(x) = 1/2m$$\omega^{2}$$x$$^{2}$$ and that $$\omega$$=2$$\pi$$f

but i can't find how to show this anywhere - not in the lecture notes, my books or the internet - I am finding this quantum mechanics course a massive step up from all the other areas of physics!

 

[malawi_glenn]

This is a problem that could be given to you in a classical mechanics course aswell.

What is the Spring-force (Hooks law), and how do you go from a (conservative)-Force to the potential?