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One end of a spring is attached to ceiling, and it is hanging straight down with a relaxed length L0. It has a spring constant k. A block of mass m is next attached to the bottom of a spring.

1. Believe how far the mass causes the spring to stretch. Identify your choice of the system, and draw a free body diagram for your system that shows all significant interactions with the surroundings. List few approximations that you must make.

2. The mass is at rest and spring has a lenght L=L0+ΔL. Starting from fundamental principles, derive an amount of stretch ΔL caused by the mass.

3. The mass is at rest and the spring has a lenght L=L0+ΔL. Call this position y=0. Suppose you grab the mass and gently pull it down an additional distance s, and at time t0 you let go. A short time Δt later, what is momentum of the block?

4. What is a new position of the block at this time (t0+Δt)?

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