The velocity of a particle executing SHM varies with displacement x as 4v² = 50 − x². The time period of oscillations is x₀/7 s. The value of x₀ is ______. [Take π = 22/7]
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

The velocity of a particle executing SHM varies with displacement x as 4v² = 50 − x². The time period of oscillations is x₀/7 s. The value of x₀ is ______. [Take π = 22/7]

G1 Physics · Accepted Answer

Rewrite as v² = (1/4)(50−x²). Comparing with v² = ω²(A²−x²), we get ω² = 1/4 and ω = 1/2 rad s⁻¹. Hence T = 2π/ω = 4π = 88/7 s. Therefore x₀ = 88.