The average energy in one time period in simple harmonic motion is

Explanation

`PE = (1)/(2) m omega^(2)y^(2) and KE = (1)/(2) m omega^(2) (A^(2) - y^(2))`
Therefore, total energy `PE + KE = (1)/(2) m omega^(2) A^(2)`
Since total energy remains constant and is equal to `(1)/(2) m omega^(2) A^(2)`. Hence average energy `= (1)/(2) m omega^(2) A^(2)`