Two particles undergo SHM along parallel lines with the same time period $T$ and equal amplitudes. At a particular instant one particle is at its extreme position while the other is at its mean position. They move in the same direction (Figure 5.95). They will cross each other after a further time:

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Take x 1 ​ = A cos ω t (from the extreme A , moving left) and x 2 ​ = − A sin ω t (from the mean, moving left). They meet when cos θ = − sin θ , so θ = 3 π /4 , i.e. t = 3 T /8 .

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