For a particle executing S.H.M., the potential energy is n times the kinetic energy when its displacement from mean position is ( 2 2 3 )A , where A is the amplitude of S.H.M. The value of n is

Step-by-step solution

The potential energy of a particle executing S.H.M. is given by U = 1 2 kx^2 and the kinetic energy is given by K = 1 2 k(A^2 - x^2) . Given that U = nK , we have: 1 2 kx^2 = n [ 1 2 k(A^2 - x^2) ] x^2 = n(A^2 - x^2) x^2(1 + n) = nA^2 n n+1 = x^2 A^2 Substituting the given displacement x = 2 2 3 A : n n+1 = ( 2 2 3 )^2 n n+1 = 8 9 9n = 8n + 8 n = 8 Answer: 8