In a simple harmonic motion, when the displacement it one- half of the amplitude, what fraction of the total energy (E) is kinetic ?

Options

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

Answer

C

Explanation

At `x=(a)/(2)` kinetic energy is
`K.E.=(1)/(2) k[a^(2)-((a)/(2))^(2)]`
`=(3)/(4)xx(1)/(2)ka^(2)`
`=(3)/(4)E`