Driven Harmonic Oscillator Model

In the Driven Harmonic Oscillator model motion takes place along the x (horizontal) coordinate axis but the springs shown in the simulation are only meant as a visual representation of a Hooke's Law force and are not a real springs.  A Hooke's Law force is zero at x=0 and the spring has almost zero length at this displacement.  In addition, the particle displacement can extend from - infinity to + infinity without the spring breaking.  These idealizations are not unrealistic because oscillatory systems without springs but that obey Hooke's Law occur often.

[Potential energy graph goes here.]

Consider a simple intermolecular bond that is approximated by a potential energy function U(r) with a local minimum a shown in the figure above.  Elementary calculus teaches us that an analytic function such as U(r) can be expanded using a power series expansion. 

[Discuss series expansion.]