When the kinetic energy of the body executing SHM is `(1)/(3)` of potential energy, the displacement is………….% of amplitude.

Options

A. `33`
B. `87`
C. `67`
D. `50`

Answer

B

Explanation

Kinetic energy of a body executing SHM
`=(1)/(2)m omega^(2) (A^(2)-x^(2))" ""………"(1)`
Potential energy `=(1)/(2) m omega^(2) x^(2)" ""…….."(2)`
Now from (1) and (2)
`(1)/(2) m omega^(2) (A^(2)-x^(2))= (1)/(3)xx(1)/(2) m omega^(2) x^(2)`
`therefore A^(2) -x^(2)= (x^2)/(3)`
`therefore A^(2)= (4x^2)/(3)`
`therefore x^(2) = (3)/(4) A^(2)`
Here `x= (A)/(2)sqrt(3) = 0.866 A`
= 87% amplitude.