Problem Diagram

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.
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