The total energy of the body executing simple harmonic motion is E . When the displacement is half of the amplitude then the kinetic energy is

Step-by-step solution

Total energy is SHM E= 1 2 m ^2 a^2 (where a= amplitude) The potential energy at displacement y is U= 1 2 m ^2 y^2 The kinetic energy is K=E-U= 1 2 m ^2 (a^2-y^2 )=E- 1 2 m ^2 y^2 Now at y= a 2 K=E- 1 2 m ^2 ( a^2 4 )=E- E 4 = 3 E 4