A body oscillates with simple harmonic motion of amplitude A . What fraction of its total mechanical energy is kinetic energy when its displacement from the mean position is A 3 ?

Step-by-step solution

Total mechanical energy of a simple harmonic oscillator is E = 1 2 m ^2 A^2 Kinetic energy at a displacement x is K = 1 2 m ^2 (A^2 - x^2) The fraction of kinetic energy to total energy is K E = A^2 - x^2 A^2 = 1 - ( x A )^2 Substituting x = A 3 : K E = 1 - ( 1 3 )^2 = 1 - 1 9 = 8 9 Answer: 8 9