Lattice vibrations with Rayleigh dissipation

We approximate a linear array of coupled harmonic oscillators as a symmetri c circular array of identical masses and springs. The springs are taken to possess mass distributed along their lengths. We give a Lagrangian formulat ion of the problem of finding the natural frequencies of oscillation for th e array. Damping terms are included by means of the Rayleigh dissipation fu nction. A transformation to symmetry coordinates as determined by the group of rotations of the circle uncouples the equations of motion.