Harmonic behavior occurs in many types of systems, including both
electronic and mechanical systems. The first step in analyzing a new
phenomenon is to choose a particular system for study which exhibits
that phenomenon. Our particular system is the simple harmonic
oscillator (SHO), the spring-and-mass system in
Figure 1. This system consists of a spring of
constant k and equilibrium length 
attaching a mass m to a
solid wall located at x=0. To keep the problem as simple as
possible, we consider motion in the x-direction only. To accomplish
this, we may consider the mass to slide on a frictionless rod oriented
in the x-direction. The motion of this system repeats periodically
in time. Our goal is to characterize and analyze this behavior.
Figure 1: Simple harmonic oscillator (SHO): spring-mass system
illustrating simple harmonic motion