For a particle performing linear S.H.M. of amplitude 'r', the potential energy is ' ' times its total energy. The displacement of particle is

Step-by-step solution

The potential energy of a particle in linear S.H.M. at a displacement x is given by U = 1 2 m ^2 x^2 . The total energy of the particle with amplitude r is given by E = 1 2 m ^2 r^2 . According to the given condition, U = E . Substituting the expressions for U and E , we get: 1 2 m ^2 x^2 = ( 1 2 m ^2 r^2 ) x^2 = r^2 x = r The displacement of the particle is r . Answer: r