If the displacement (x) and velocity (v) of a particle executing simple harmonic motion are related through the expression `4v^2=25-x^2`, then time period is,

Options

A. `pi sec`
B. ` 2 pi sec`
C. `4 pi sec`
D. `6 pi sec`

Explanation

`V^2=25-x^2`
`V^2=25/4-(x^2)/4`
`V=1/2sqrt(25-x^2`
`V=omegasqrt(A^2-x^2`
On comparing equations (1)and(2),
`omega =1/2`
`implies (2pi)/T=1/2`
`therefore T=4pi s`