As an important application and extension of the foregoing ideas, and to obtain a first glimpse of wave phenomena, we consider the following system. Suppose we have N identical particles of mass m in a line, with each particle bound to its neighbors by a Hooke’s law force, with “spring constant” k. Let us assume the particles can only be displaced in one-dimension; label the displacement from equilibrium for the jth particle by qj , j = 1, ...,N. Let us also assume that particle 1 is attached to particle 2 on the right and a rigid wall on the left, and that particle N is attached to particle N 1 on the left and another rigid wall on the right.
linear chain, coupled oscillator, chapter 4, four
Physical Sciences and Mathematics | Physics
Torre, Charles G., "04 Linear Chain of Coupled Oscillators" (2014). Foundations of Wave Phenomena. Book 19.