Hooke's Law(HL) model
HL model is different because, unlike the other models, it admits an exact solution. In Hooke's law the force is proportional to the displacement of the particle from its equilibrium position and it is directed towards the equilibrium position. As you can see from the example below, the vibration of a mass about equilibrium typifies the motion of a particle subject to an HL force. You can also view a movie of the relationship between the spring model, force-displacement, and the potential of the Hookean Model.
For a more complete explanation of the HL model read "Molecular Dynamics: An Introduction" by Lloyd Fosdick.