When you displace an object by an amount x from its equilibrium, a restoring force acts on it/ tending to return the object to its equilibrium position. the magnitude of the restoring force can be a complicated function of x. In such cases, we can generally imagine the force function F(x) to be expressed as a power series in x as . The first term here is just hooks law, which describes the force exerted by a simple spring for small displacements. for small excursions from equilibrium, we generally ignore the higher-order terms, but in some cases, it is desirable to keep the second term as well. If we model the restoring force as , how much work is done on an object in displacing it from x=0 to x= xmax by an applied force -F?
