Two beads, each of mass , are joined by a single light spring of stiffness and are…
PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Oscillations and normal modes · Oscillations and normal modes
Action and Symmetry, Ch Small oscillations: stability, degeneracy, symmetry and spectra
Problem
Two beads, each of mass m, are joined by a single light spring of stiffness κ and are otherwise free: nothing else touches them, and motion is confined to a frictionless horizontal plane so that gravity does no work on any displacement considered. Each bead has two coordinates.
((a)) State the total number of independent coordinates.
((b)) Before writing any equation of motion, predict the number of zero-frequency modes, and identify each with a translation or a rotation of the pair as a whole.
((c)) State how many vibrational (nonzero) frequencies remain, and say whether the symmetry of this system can force any of them into a degenerate pair.