Two particles execute simple harmonic motion of the same amplitude and frequency along the same straight line. They pass one another when going in opposite directions each time their displacement is half their amplitude. Find the phase difference between them.

So, wt = π/3
The same constraint happens for x2, except that is moving in the other direction. So the closest value is wt+? = 2π/3.
To find out the phase difference ? between them, substitute π/3 for wt ion the equation wt+? = 2π/3,
wt+? = 2π/3
π/3+? = 2π/3
or, ? =2π/3 - π/3
= π/3
From the above observation we conclude that, the phase difference between the two particles will be π/3.