Electric Potential & electron oscillation

[eoghan]

Hi there!
I have this problem:
How to calculate the frequency of the oscillations of an electron from its equilibrium point in this potential:
V(z)=k/(2ɛ)*[sqrt(z^2 - 9R^2) - sqrt(z^2 - r^2)]*sgn(z)

 

[G01]

What have you tried so far? You need to show work if you want to get help here.

 

[eoghan]

I've tried to use the conservation of energy: I can get the length of the oscillation, but I can't get the time.
I've tried to solve the differential equation F=ma calculating the electric field, but I can't solve it...
I don't know what to do