Molecular movement, potential energy and angular frequency

[smhippe]

Homework Statement

The relative motion of two atoms in a molecule can be described as the motion of a single body of mass m = 3 x 10-26 kg moving in one dimension, with a potential energy given by the equation
U(r)=(A/(r^12))-(B/(r^12))
n this equation A = 10^10 J m^12 and B = 10^20 J m^6 are positive constants and r is the separation between the atoms. This potential energy function has a minimum value at r=r0, which corresponds to an equilibrium separation of the atoms in the molecule. If the atoms are moved slightly, they will oscillate around this equilibrium separation. What is the log10 of the angular frequency of these oscillations?

The Attempt at a Solution

I really don't understand this. I looked up an equation that related potential gravity to SHM. I think that is a good start right? So I can set potential energy U(r) equal to this equation
U(t)=(1/2)(a^2)cos^2(wt+\varphi). The problem is U(t) is a function of time not position. So could I differentiate one of these equations to get the right one? Or am I completely wrong in my thought process?

 

[smhippe]

Sorry about that, I'm trying to avoid using the equation editor...
(A/r^12)-(B/r^6)
Hopefully that makes some more sense.

 

[zachzach]

You can solve for r_0 since you know u(r) has a minimum there. You need to get an equation of the form F = -kr so approximate the function around r_0, and remember F = -\frac{du(r)}{dr}.