So far, our mass-spring chains have only been allowed to move in the vertical direction.
(a) Set up the system governing the planar motions of a mass-spring chain consisting of two unit masses attached to top and bottom supports by unit springs, where the masses are allowed to move in the longitudinal and transverse directions. Compare the resulting vibrational frequencies with the one-dimensional case.
(b) Repeat the analysis when the bottom support is removed.
(c) Can you make any conjectures concerning the planar motions of general mass-spring chains?