The total energy of the body executing SHM is E. the, the kinetic energy when the displacement is half of the amplitude is

Options

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

Answer

C

Explanation

Total energy is SHM,
`E = (1)/(2)m omega^(2)a^(2)`, (where, a = amplitude)
Kinetic energy, `K = (1)/(2)m omega^(2)(a^(2)-y^(2))=E-(1)/(2)m omega^(2)y^(2)`
When `y = (a)/(2)`
`rArr" "K = E - (1)/(2)m omega^(2)((a^(2))/(4))=E - (E)/(4)=(3E)/(4)`