A particle executes `SHMx=Asin(omegat+phi)`. At `t=0`, the position of the particle is `x=(sqrt3A)/(2)` and it moves along the positive x-direction. Find
(a) phase constant `phi`
(b) velocity at `t=pi/omega`
(c) acceleration at `t=pi/omega`

Explanation

`x=Asin(omegat+phi)`
At `t=0, x=(sqrt3A)/(2)`
`sqrt3A/2=Asin(omegaxx0+phi)impliessinphi=sqrt3/2`
`=sin60^@` or `120^@`
`phi=60^@` or `120^@`
`v=(dx)/(dt)=Aomegacos(omegat+phi)`
At `t=0, v=Aomegacosphi`
`cos60^@=1/2` and `cos 120^@=-1/2`
As v is `+ve` at `t=0`, `phi=60^@=pi/3`
(b) Now `x=Asin(omegat+pi//3)`
`v=Aomegacos(omegat+pi//3)`
At `t=pi//omega`, `x=Asin(omega*pi//omega+pi//3)`
`=-Asinpi/3=(-sqrt3A)/(2)`
`v=Aomegacos(omega*pi/3+pi/3)=-Aomegacospi//3=-(Aomega)/(2)`
(c) `a=-omega^2x`
At `t=pi/omega, x=(-sqrt3A)/(2)`
`a=-omega^2(-(sqrt3A)/(2))=(sqrt3omega^2A)/(2)`