Two particles have displacements x₁ = A sinωt and x₂ = A sin(ωt+π/3). What is the maximum possible separation between them?
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Question

Two particles have displacements x₁ = A sinωt and x₂ = A sin(ωt+π/3). What is the maximum possible separation between them?

G1 Physics · Accepted Answer

The separation is x₂−x₁ = A[sin(ωt+π/3)−sinωt]. Using sinC−sinD = 2cos[(C+D)/2]sin[(C−D)/2], we get x₂−x₁ = 2A cos(ωt+π/6) sin(π/6) = A cos(ωt+π/6). Therefore its maximum magnitude is A. Correct option: B.