Conservation of Energy

In a closed system energy is conserved.

The position of the blue ball ,there is the Potential Energy (PE) while the Kinetic Energy (KE) = 0.

As the blue ball is approching the purple ball position the PE is decreasing while the KE is increasing. At exactly halfway between the blue and purple ball position the PE = KE.

The position of the purple ball is where the Kinetic Energy is at its maximum while the Potential Energy (PE) = 0.

At this point, theoretically, all the PE has transformed into KE> Therefore now the KE = 19.6J while the PE = 0.

The position of the pink ball is where the Potential Energy (PE) is once again at its maximum and the Kinetic Energy (KE) = 0.

PE + KE = 0

PE = -KE

The sum of PE and KE is the total mechanical energy:

Total Mechanical Energy = PE + KE