Drop-tubes are used to simulate weightlessness for various experiments. The experiment container is stopped at the bottom of the tube by a spring and damper. Since the equipment can be quite delicate, the deceleration of the container, and hence its motion, is very important.

What is known:

container mass m = 17 kg

impact velocity v = 13 m/s

spring constant k = 715 N/m

damper constant c = 100 N-s/m

Question

What is the motion of the container after it impacts the spring and damper at the bottom of the tube?

Approach

Determine the differential equation of motion.

Solve the equation of motion for the displacement.

Apply the initial conditions.

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