### Energy of a Vertical Mass/Spring System

A 2-kg mass hangs from a massless spring of spring constant k = 5 N/m. The spring has an equilibrium (unstretched) length of 13 m. The displacement of the spring from equilibrium is shown in meters, and the velocity of the mass is shown in m/s. Pull down or push up on the end of the spring to displace the mass from its initial position, and then push "Play" to watch it move up and down. Study the graphs of kinetic energy, gravitational potential energy, spring potential energy, and total energy as functions of time. Can you verify that these energies are calculated correctly? What can you conclude?

### Hints

1. When (where) does the gravitational potential energy have its maximum value? Its minimum value?
2. When (where) does the spring's potential energy have its maximum value? Its minimum value?
3. When (where) does the mass's kinetic energy have its maximum value? Its minimum value?
4. How (why) do each of  these types of energy change?
5. What should be true, according to the Law of Energy Conservation?

### Reference

See Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Section 8.4

Illustration written by Steve Mellema