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The Conservation of Mechanical Energy

Definition: Mechanical energy is the kinetic energy plus all of the kinds of potential energy that are present. In the absence of non-conservative forces, mechanical energy is conserved. Example: if gravitational and spring forces are present:
KEi + PEgi + PEsi = KEf + PEgf + PEsf.      (6)
Notice that while the total amount of energy is conserved, the distribution of energy may change. For example, there may be more KE in the initial state and more PE in the final state (or the other way around).