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A spring-mass system is initially at rest is shown above. A mass m = 1.0 kg traveling at 12ms collides and sticks to the mass that is attached to the spring. Suppose k = 1000N m and M = 3.0 kg.

1. Calculate the speed of the two masses immediately after the collision.

2. Calculate the maximum distance the spring will be compressed.

3. Is the system a simple harmonic oscillator? Prove by stating the appropriate equation describing the system.

4. If the system is a simple harmonic oscillator calculate the period of oscillation of the system. If not, qualitatively describe the motion of the system for one oscillation.

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