A particle executes simple harmonic motion of amplitude A along the X-axis. At t=0 the position of the particle is `x=A/2` and it moves along the positive x-direction. Find the phase constant `delta` if the equation is written as `x=Asin(omegat+delta)`

Explanation

We have `x=sin(omegat+delta).At t=0, x=A/2`
Thus `A/2=Asindelta`
`or `sindelta=1/2`
or `delta=pi/6 or 5pi/6`
The velocity ils `v =(dx)/(dt)=Aomegacos(omegat+sigma)`
At `t=0, v=Aomega cosdelta`
Now, `cospi/6=sqrt3/2 and cos (5pi)/6=-sqrt3/2`
A v is positive at `t=0, delta` must be equal to `pi/6`