The amplitude of a particle executing S.H.M. is 3 ~cm . The displacement at which its kinetic energy will be 25 % more than the potential energy is

Step-by-step solution

aligned & Given : K.E = P.E + 25 100 . P . E & ~K . E = P . E + 1 4 P . E & We know K . E = 1 2 ~m ^2 ( ~A ^2- x ^2 ) and P E = 1 2 ~m ^2 x ^2 & K . E = 5 4 P.E & 1 2 m ^2 (A^2-x^2 )= 5 4 ( 1 2 m ^2 x^2 ) & A ^2- x ^2= 5 4 x ^2 & ~A ^2= 9 4 x ^2 & A = 3 2 x & x = A 2 3 =2 ~cm & aligned