Potential energy of a simple harmonic oscillator U=21mω2y2
Kinetic energy of a simple harmonic oscillator K=21mω2(A2−y2)
Here y= displacement from mean position A= maximum displacement (or amplitude) from mean position
Total energy is E=U+K =21mω2y2+21mω2(A2−y2) =21mω2A2
When the particle is half way to its end point ie, at half of its amplitude then y=2A
Hence, potential energy U=21mω2(2A)2 =41(21mω2A2) U=4E