For the two SHM particles x₁ = A sinωt and x₂ = A cosωt, find the first positive time when their speeds are equal. Also identify the relation between their velocity directions at that instant.
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Question

For the two SHM particles x₁ = A sinωt and x₂ = A cosωt, find the first positive time when their speeds are equal. Also identify the relation between their velocity directions at that instant.

G1 Physics · Accepted Answer

Equal speeds require |v₁| = |v₂|. Thus, |cosωt| = |sinωt|. The first positive solution is ωt = π/4. Therefore, t = T/8. At this instant, v₁ = +Aω/√2, v₂ = −Aω/√2. So their speeds are equal but the velocities are opposite. Correct option: B.