Question

What is the ratio of kinetic energy to potential energy when the displacement of a particle is one half of its amplitude ?

Answer 1

Let Total energy be E= (1/2)K(Xm)²

According to question, displacement x= (Xm)/2

We know that potential energy U= (1/2)Kx²

                                                    U=(1/2)K(Xm/2)²

                                                       =(1/2)K(Xm)²/4

                                                       =E/4

So Kinetic energy would be,

K.E= E-U

      =E-(E/4)

      =3E/4

Therefore ratio of K.E and P.E is = (K.E)/U= {3E/4}/{E/4}

                                                                    =3:1