The displacement of a particle executing S.H.M. is given by `y = 10 sin [6t + (pi)/(3)]` where y is in metres and t is in seconds. Then the initial displacement and velocity of the particle is

Options

A. `5sqrt(3) m and 30 m s^(-1)`
B. `20sqrt(3) m and 30 m s^(-1)`
C. `15sqrt(3)m and 30 m s^(-1)`
D. `15 m and 5 sqrt(3) m s^(-1)`

Answer

A

Explanation

At `t=0,y=10sin(6(0)+(pi)/(3))`
`=10xx(sqrt(3))/(2)=5sqrt(3)m`
As `v=(dy)/(dt)=60cos(6t+(pi)/(3))`
At `t=0,v=60cos(0+(pi)/(3))=60xx(1)/(2)=3m//s`