When the displacement in S.H.M in 1/3 of amplitude. when the friction of the total energy is kinetic energy and potential energy?

The total energy is given as

E = PE + KE = (1/2)kA2

now,

PE = (1/2)kx2

here

x = A/3

thus,

PE = (1/2)k.(A/3)2

 = (1/18)kA2

so,

PE = (1/9).[(1/2)kA2]

or

PE = E/9

and so, kinetic energy

KE = E - PE = E - E/9

so,

KE = (8/9).E

Regards

Arun (askIITians forum expert)