For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at a certain displacement ' x ' from the mean position. If ' A ' is the amplitude of S.H.M., the value of ' x ' is

Step-by-step solution

The potential energy of a particle executing S.H.M. at a displacement x from the mean position is given by U = 1 2 m ^2x^2 The kinetic energy of the particle at displacement x is given by K = 1 2 m ^2(A^2 - x^2) Given that the potential energy is 8 times the kinetic energy: U = 8K 1 2 m ^2x^2 = 8 1 2 m ^2(A^2 - x^2) x^2 = 8(A^2 - x^2) x^2 = 8A^2 - 8x^2 9x^2 = 8A^2 x^2 = 8 9 A^2 x = 2 2 3 A Answer: 2 2 3 A