Six-light-springs.connected to a small copper sphere-of mass m-as shown-in-the-following figure. The spring constants are in-the ratio-k = 9: k2 = 16: k3 = 25,·therefore the potential-energy function can-be written as T%D1V(x, y, z) = k(9x² + 16y² + 25z²)¶At-timet = 0 the sphere receives a push-in the(1,1,1)'direction that-imparts to-it a speed v, atthe origin. Given that-k = n?m¶(a) What are-the x, y and z·components of thedifferential equations of motion for the sphere?|(b).Find x, y, and z as functions of the-time·t.(c)-Does the sphere everrepeat its path?¶(d)-If so, for what value oft does it first return to the origin with the same velocity:that it had at·t = 0?¶elleeeFeeel

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