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Simple harmonic motion of a mass on a spring, released at rest at maximum displacement. Develop x(t) and v(t).

On a frictionless table, a spring whose force constant is 60 nt/m has one end fixed and the other attached to mass M= 3.9 kg. A cord connects mass M to a suspended rock whose mass is m= 3.2 kg. Assume an x axis origin at the movable end of the spring when the spring contains no potential energy. At some instant, with the system stationary, the cord is cut and mass M begins simple harmonic motion.
See ATTACHMENT #1 for a diagram showing parameters.
Find the x coordinate and the velocity of the movable end of the spring exactly .60 sec after the cord is cut.


Solution Preview

Step 1.
Note: In the original equilibrium the force exerted on the end of the spring is equal to the weight of the rock. The relation between F, the force exerted on a spring and x, the distance from the x origin at its unstressed end, is expressed by:
(1) F = k x
Step 2. Since F = m g, the weight of the rock, and k is given, you should ...