The total mechanical energy of a particle executing simple harmonic motion is `E` when the displacement is half the amplitude of its kinetic energy will be

Options

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

Answer

A

Explanation

`E = (1)/(2) m omega^(2) A^(2) and K.E. = (1)/(2) m omega^(2)(A^(2) - x^(2))`
Putting`x = (A)/(2) or x^(2) = (A^(4))/(4)`
`K.E. = (1)/(2) m omega^(2) (A^(2)- (A^(2))/(4))= (3)/(4)[(1)/(2) m omega^(2)(A^(2))] = (3E)/(4)`