A particle performing `SHM` having amplitude 'a' possesses velocity `((3)^(1//2))/(2)` times the velocity at the mean position. The displacement of the particle shall be

Options

A. `(a)/(2)`
B. `(3)^(1//2) (a)/(2)`
C. `((a)/(2))^(1//2)`
D. `(2)^(1//2) a`

Answer

A

Explanation

`V = omega sqrt(a^(2) - x^(2))`
`(sqrt(3))/(2)a omega = omega sqrt(a^(2) - y^(2))`
`y^(2) = (1)/(4)a^(2)" "y = (a)/(2)`