A bead at the bottom of a bowl is one example of an object in a stable equilibrium position. When a physical system is displaced by an amount x from stable equilibrium, a restoring force acts on it, tending to return the system to its equilibrium configuration. The magnitude of the restoring force can be a complicated function of x. For example, when an ion in a crystal is displaced from its lattice site, the restoring force may not be a simple function of x. In such cases we can generally imagine the function F(x) to be expressed as a power series in x, as F(x) = ─(k1x + k2x2 + k3x3 + . . .). The first term here is just Hooke’s law, which describes the force exerted by a simple spring for small displacements. For small excursions from equilibrium we generally neglect the higher order terms, but in some cases it may be desirable to keep the second term as well. If we model the restoring force as F =─ (k1x + k2x2), how much work is done in displacing the system from x = 0 to x = xmax by an applied force ─F?