A small lead ball of mass m is suspended by means of six light springs as shown in Figure...

A small lead ball of mass m is suspended by means of six light springs as shown in Figure 4.4.1. The stiffness constants are in the ratio 1:4:9, so that the potential energy function can be expressed as

At time t = 0 the belli receives a push in the (1, 1, 1) direction that imparts to it a speed v0 at the origin. If k = π2m, numerically find x, y, and z as functions of the time t. Does the ball ever retrace its path? If so, for what value of t does it first return to the origin with the same velocity that it had at t = 0?