Two particles P₁ and P₂ execute SHM along the same straight line about the same mean position. Their displacements are x₁ = A sinωt and x₂ = A cosωt. At t = 0 they are at different positions. What is the first positive time at which they meet?
Options

Question

Two particles P₁ and P₂ execute SHM along the same straight line about the same mean position. Their displacements are x₁ = A sinωt and x₂ = A cosωt. At t = 0 they are at different positions. What is the first positive time at which they meet?

Options

G1 Physics · Accepted Answer

The particles meet when x₁ = x₂. Therefore, A sinωt = A cosωt. Thus, tanωt = 1. The first positive solution is ωt = π/4. Using ω = 2π/T, t = (π/4)/(2π/T) = T/8. Correct option: B.