ABSTRACT
This chapter explores the properties of coupled harmonic oscillators. These systems can be analyzed by using either the Lagrangian approach, or alternatively using Newton’s second law. The simplest form of these systems in mechanics contains two masses connected by springs to each other. A second simple example of coupled mechanical oscillators is the double pendulum, which also exhibits a wide range of interesting behaviors. The discussion of the two-mass system will lead us to a more general description of linearly coupled harmonic systems, and how their equations of motion can be written in matrix form. The best way to obtain solutions to the equations of motions for coupled oscillations is by using standard techniques from linear algebra, in order to find the eigenvalues and eigenvectors of a matrix. Systems of coupled harmonic oscillators can be analyzed by using either the Lagrangian approach, or alternatively using Newton’s second law.
