The displacement of a particle executing SHM is given by ` y=10 sin(6t+pi//3)` in metre and time t in second.The initial displacement and the velocity of the particle are respectively.

Options

A. `5 sqrt3 m and 30 ms^-1`
B. ` 15 m and 5sqrt3 ms^-1`
C. ` 15 sqrt3 m and 30 ms^-1`
D. ` 20sqrt3 m and 30 ms^-1`

Answer

a

Explanation

`y=10 sin(6t+pi//3)m`
`implies A=10m,omega=6rads^-1 and phi=pi/3`
For initial displacement,`t=0`,
`y=10sin(6xx0+pi//3`
`=10xxsqrt(3)/(2)`
`therefore y=5sqrt(3)m`
Velocity,`V=Aomega cos phi`
`V=10xx6xxcos(pi//3)`
`=6xx1//2`
`therefore V=30 ms^-1`