Two particles move parallel to the x-axis about the origin with same amplitude 'a' and frequency ω. At a certain instant they are found at a distance a/3 from the origin on opposite sides but their velocities are in the same direction. What is the phase difference between the two?

Let x1=asin⁡ωt and x2=asin⁡(ωt+δ) be two SHMs. a3=asin⁡ωt  and  −a3=asin⁡(ωt+δ)sin⁡ωt=1/3  and  sin⁡(ωt+δ)=−1/3 Eliminating t,13cos⁡δ+1−19sin⁡δ=−139cos2⁡δ+2cos⁡δ−7=0cos⁡δ=−1  or  79i.e., δ=180∘  or  cos−1⁡79If we put 180o, we find that v1 and v2 are of opposite signs.Hence δ = 180o is not applicable.∴ δ=cos−1⁡79