Two particles P₁ and P₂ perform SHM on the same line according to x₁ = A sinωt and x₂ = A cosωt. What is the maximum possible distance between the two particles during their motion?
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Question

Two particles P₁ and P₂ perform SHM on the same line according to x₁ = A sinωt and x₂ = A cosωt. What is the maximum possible distance between the two particles during their motion?

G1 Physics · Accepted Answer

Their relative displacement is x₁−x₂ = A(sinωt−cosωt). Using sinθ−cosθ = √2 sin(θ−π/4), we obtain x₁−x₂ = √2A sin(ωt−π/4). Hence the amplitude of relative motion is √2A. Therefore the maximum separation is √2A. Correct option: B.