In a diatomic molecule, one atom is very much heavier than the other and the lighter atom is free to move on a straight line through the centre of the heavier atom. The potential energy for the force between two atoms in a diatomic molecule can be represented approximately by

where x is the atomic separation and a and b are positive constants.
i) Locate any positions of stable equilibrium of the lighter atom.
ii) Find the period of small oscillations about such positions, assuming the mass of the lighter atom is m.
iii) Sketch the potential energy as a function of x. How does the force vary as the atoms approach each other?