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

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

• Determine the differential equation of motion.
• Solve the equation of motion for the displacement.
• Apply the initial conditions.