Oscillations and Simple Harmonic Motion

Waves begin with oscillations. An oscillation is any motion that repeats itself over a regular interval of time, such as a mass bouncing on a spring, a child on a swing, or the vibration of a guitar string. To understand traveling waves, we first study the simplest and most important kind of repetitive motion: simple harmonic motion (SHM).

An object undergoes simple harmonic motion when the net force acting on it is always directed toward a fixed equilibrium position and is directly proportional to the displacement from that position. Mathematically, this restoring force obeys $F = -kx$, where $x$ is the displacement, $k$ is a positive constant, and the minus sign indicates that the force always opposes the displacement. Because acceleration is proportional to force, this is equivalent to