A bob is attached to the unstreached end of a spring. The bob is then released with no initial velocity. Initially, the system (of the bob and the spring) have no kinetic energy KE, no spring potential energy PE_s, and no gravitational potential energy PE_g. 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:

• The total mechanical energy is conserved even though its numerical value is zero. The sum total of the KE, PE_s, PE_g always add up to zero because of the initial conditions chosen. If fact, since only PE_g can be negative, this means that |PE_g| = KE + PE_s in this special case.
• The bob will oscillate around the equilibrium position - the position where the bob would hang motionless on the spring. This is the position were the force of the spring F_s is equal to the weight of the bob mg. This is always true for any oscillating system undergoing simple harmonic motion.