Consider a general potential energy function, U(r), for a force F=−(dU/dr)r^ on a particle of mass m. Assume that the origin (r=0) is a point of stable equilibrium. By expanding U(r) in a Taylor series about the origin, show that if a particle is displaced slightly from the origin and then released, it will undergo simple harmonic motion about the origin. This explains why the linearization procedure of Section 14.3 is guaranteed to result in sinusoidal oscillations.