The potential energy of a simple harmonic oscillator, when the particle is half way to its end point is

Step-by-step solution

Potential energy of a simple harmonic oscillator U= 1 2 m ² y² Kinetic energy of a simple harmonic oscillator K= 1 2 m ² (A²-y² ) Here y= displacement from mean position A= maximum displacement (or amplitude) from mean position Total energy is aligned E &=U+K &= 1 2 m ² y²+ 1 2 m ² (A²-y² ) &= 1 2 m ² A² aligned When the particle is half way to its end point ie, at half of its amplitude then y= A 2 Hence, potential energy aligned U &= 1 2 m ² ( A 2 )² &= 1 4 ( 1 2 m ² A² ) U &= E 4 aligned