A particle is describing simple harmonic motion. If its velocities are v1 and v2 when the displacements from the mean position are y1 and y2 respectively, then its time period is?

In simple harmonic motion, velocity v = ω√(A² - y²) ∴ v₁ = ω√(A² - y₁²) ⇒ v₁² = ω²(A² - y₁²) (i) and v₂ = ω√(A² - y₂²) ⇒ v₂² = ω²(A² - y₂²) (ii) Solving equations (i) and (ii), we get v₂² - v₁² = ω²(y₁² - y₂²) ω = √(v₂² - v₁²)/(y₁² - y₂²) ⇒ T = 2πω = 2π√(y₁² - y₂²)/(v₂² - v₁²).