Two particles A, B, each of mass m, are connected by a spring with spring constant k and natural length l. In addition, particle A is connected by a spring to a fixed point P while B is connected by another spring to a fixed point Q. All three springs are identical. The distance PQ = 3a > 3l. Find the frequencies of the longitudinal modes of the system and describe the associated normal mode oscillations. What happens when a < l? [Longitudinal oscillations take place along the line PQ. Ignore gravity.]