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# Physics sample question: Compressed spring question

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On a frictionless table, a spring has one end fixed and the other attached to block M. Block m, is in contact but not attached to M.
The spring, originally unstressed was compressed from 0 to -S. There the spring system was released from rest. See ATTACHMENT for a diagram with parameters and basic physics.
Block M= 2.0 kg, block m= 1.7 kg, k= 60 nt/m, and S= .50 m.
a. From release, find the time until the blocks separate, and also their velocity at that instant.
b. Find Xm, the new amplitude of the SHM after the blocks separate.
c. Develop x(t) for the SHM of block M with separation at time t=0.

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Solution:
Physics statements:
A. Initially, at rest at -S, both blocks are pushed toward 0.
B. Between -S and 0 the acceleration is rightward, but not constant since the force exerted by the spring decreases, becoming zero at location x=0 .
C. After M passes x=0, the spring pulls to the left on block M so block M acquires leftward acceleration beyond x=0, so they separate, and block m continues to the right with the velocity it had at at x=0.
D. Block m removes (kinetic) energy from the system, so the new energy total for the system is the kinetic energy of block M at x=0 when the new SHM, with only block M, begins.
E. For the new SHM, initial conditions at t=0 are with block M at x=0 with maximum, positive velocity.
F. The new ...

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