The properties of periodic motion recur in many areas of physics, including mechanics, quantum physics, and electricity and magnetism. The ubiquity of oscillatory motion in biological and chemical systems, as well as engineering, provides interdisciplinary importance for developing the formal description of periodic motion. We will explore the physical principles and fundamental mathematics related to periodic motions. Topics will include damped and forced harmonic motion, normal modes, the wave equation, Fourier series and integrals, and complex analysis. Principles and techniques developed in this course are central to many subsequent courses, particularly Quantum Mechanics (PHYS214, PHYS315), Classical Dynamics (PHYS313), and Electricity and Magnetism (PHYS324). An important component of this course is to develop the ability to use mathematical software packages to graph expressions, solve equations, and obtain numerical solutions to differential equations.