A particle is executing linear simple harmonic motion of amplitude 'A'. The fraction of the total energy is the kinetic when the displacement is half of the amplitude is

Options

A. `(1)/(4)`
B. `(1)/(2sqrt(2))`
C. `(1)/(2)`
D. `(3)/(4)`

Answer

D

Explanation

`KE=(1)/(2)momega^(2)(A^(2)-x^(2))`
`=(1)/(2)momega^(2)(A^(2)-(A^(2))/(4))=(3)/(4)xx(1)/(2)momega^(2)A^(2)`
`therefore KE=(3)/(4)T.E.`