When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes to be (1/6)kA^2. For the average kinetic energy over the same range and direction, it is (1/3)kA^2, which is double the average potential energy. What the physical explanation of the different average values of PE and KE? P.S. No mathematical explanations please, i.e. area under the graph, etc, only explanations in terms physics of the event are appreciated. The question does not involve time averages of PE and KE. Snapshots of derivations can be uploaded if requested.