For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at 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

Potential energy: U= 1 2 m ^2 x^2 and Kinetic energy: K= 1 2 m ^2 (A^2-x^2 ) Given: Potential energy =8 Kinetic energy aligned & U =8 ~K & 1 2 ~m ^2 x ^2=8 1 2 ~m ^2 ( ~A ^2- x ^2 ) & x ^2=8 ~A ^2-8 x ^2 & 9 x ^2=8 ~A ^2 & x ^2= 8 ~A ^2 9 & x = 2 2 ~A 3 aligned