Setup: A bob is attached to the unstreached end of a spring. The bob is then lifted .2 m and given an upward velocity of 1 m/s. The zero reference point for the potential energy is taken to be the location of the end of the spring when it is unstreached.

Points to observe:

• Initially, the system (of the bob and the spring) have non-zero values of kinetic energy KE, spring potential energy PE_s, and gravitational potential energy PE_g.
• Although the KE, PE_s, PE_g are all changing with time, their sum total, the mechanical energy ME is constant because Energy is conserved when there is no frictional losses or external work done on the system. The external work needed to lift and set the bob into motion initially is equal to ME.
• The gravitational potential energy PE_g can become negative because we chose zero reference level to be the position of the spring before the bob was attached. To make PE_g always positive we would have to choose the zero reference point to be the bottom of bob's motion which changes depending upon the initial conditions.
• The large positive bumps in the springs PE_s occurs when the bob is below the zero reference level. Because PE_s depends upon the displacement squared, it is always positive regardless of weather the bob is above or below the position of the unstreached spring, the zero reference level.
• Also see the Oscillating Beans Problem Example problem.
• It is even possible to arrange the thing so that the total mechanical energy ME is equal to zero and still have the bob oscillate. Just let the bog go from the unstreached position of the spring with no velocity. Zero ME QT Movie (312K)