The maximum potential energy of a block executing S.H.M. is E and amplitude of oscillation is 'A'. The kinetic energy of the block at amplitude A/2 is

Step-by-step solution

The maximum potential energy of a block executing simple harmonic motion is given by E = 1 2 k A^2 , which is also equal to the total energy of the system. The kinetic energy of the block at any displacement x is given by K = 1 2 k (A^2 - x^2) . Substituting x = A 2 into the kinetic energy expression: K = 1 2 k (A^2 - ( A 2 )^2 ) K = 1 2 k (A^2 - A^2 4 ) K = 1 2 k ( 3A^2 4 ) K = 3 4 ( 1 2 k A^2 ) Since E = 1 2 k A^2 , we get: K = 3 E 4 Answer: 3 E 4