Chapter 6: Small Oscillations

Many problems involve small displacements from a stable equilibrium position, with a system-dependent restoring force that seeks to drive the system back to equilibrium. The problems may also include additional external forces or internal friction, etc. In many instances, the system’s response produces small oscillations or vibrations about the equilibrium point. Simple examples are a small ball rolling around the bottom of a bowl or an atom or molecule distorted by a weak external electric or magnetic field. In this part, we consider situations for systems where the unperturbed system can be described in terms of a potential. To illustrate the basic approach, we first look at the one-dimensional case.