In case of simple harmonic motion –
(A) What fraction of total energy is kinetic and what fraction is potential when displacement is one half of the amplitude.

Explanation

In S.H.M.
`K.E. = (1)/(2) K (A^2 - X^2)" "P.E. =(1)/(2) Kx^2`
`T. E. = (1)/(2) KA^2`
(A) `f_(K.E.)= (K.E.)/(T.E.)=(A^2 - X^2)/(A^2)` at `x= (A)/(2)`
`f_(K.E.)= (A^2 - A^2 //4 )/(A^2) = (3)/(4)`
`f_(P.E.)= (P.E.)/(T.E.)= (X^2)/(A^2)` at `x= (A)/(2)`.
`f_(P.E.)= (A^2 //4)/(A^2 )= (1)/(4)`