Two bodies of masses m and 3m are attached to each other and to two fixed points by three identical light springs as shown in figure

The whole arrangement rests on a smooth horizontal table. The springs are stretched so that the tension in each spring is T and its length is L (much greater than its unstretched length). Show that the angular frequencies of the normal modes for longitudinal oscillations of small amplitude are given by

w2 = 4 + ?7/3 T/mL.

Describe the motions of the two bodies for each normal mode.

m 3m fi