Two particles execute SHM of the same amplitude and frequency on parallel lines side by side. They cross each another when moving in opposite directions each time their displacement is half their amplitude. What is the phase difference between them ?

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$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{6}$

$\frac{2 π}{3}$

answer is B.

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Detailed Solution

At $y = \frac{A}{2}$ they are in opposite direction
$\begin{array}{l} \frac{A}{2} = Asin ϕ_{1}; ϕ_{1} = 30^{0} = \frac{π}{6} \\ and ϕ_{2} = π - \frac{π}{6} = \frac{5 π}{6} \\ Δϕ = ϕ_{1} - ϕ_{2} = \frac{2 π}{3} \end{array}$

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