All parts of possible

1. Consider a linear array of N identical simple pendulums of mass m and length & that are suspended from equal-height points, evenly spaced a distance a apart. Suppose that each pendulum bob is attached to its two immediate neighbors by means of light springs of un- stretched length a and spring constant K. The following figure shows a small part of such an array. Let x, = ja be the equilibrium position of the jth bob for j E {1,. .., N}, and let ; be its horizontal displacement. Assume that |;|