Two particles execute SHM on the same line according to x₁ = A sinωt and x₂ = A cosωt. Which statements are correct?
Select all that apply

Question

Two particles execute SHM on the same line according to x₁ = A sinωt and x₂ = A cosωt. Which statements are correct?

G1 Physics · Accepted Answer

For meeting, sinωt = cosωt, giving t = T/8. Relative displacement has amplitude √2A. Equal velocities require cosωt = −sinωt, giving t = 3T/8. Equal speeds first occur at ωt = π/4, so t = T/8, and the velocity signs are opposite. Therefore all four statements are correct.