Question

The phase of a particle in SHM at time t is pi/6. The following inference is drawn from this:
1. The particle is at x=a/2 and moving in + X direction

2. The particle is at x=a/2 and moving in - X direction

3. The particle is at x= -a/2 and moving in + X direction

4. The particle is at x= -a/2 and moving in - X direction

PLEASE GIVE THE SOLUTION / EXPLAIN THE ANSWER!!

Answer 1

option 1.

Let   x = A sin (ω t + Ф)
            Given  ω t + Ф = π/6
So  x  = A /2   

dx / dt = v = A ω cos (ω t + Ф) = A ω √3/2

Since  x and y are positive, the particle is at  x = A/2 and moving in +x direction.