Now let's do the problem with the system as the stone, spring and earth.  What is the change in energy within the system?  (How much energy enters or leaves the system?)
 
 
 

Now we must define some new types of energy.  If we are not allowing energy to flow in or out of the system then, the energy is in some other form within the system after is has been converted from kinetic energy.  These "stored" energies are the potential energies.