A particle executes SHM along the x-axis. At distances x₁ and x₂ from the mean position, its velocities are v₁ and v₂ respectively. The time period is:
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Question

A particle executes SHM along the x-axis. At distances x₁ and x₂ from the mean position, its velocities are v₁ and v₂ respectively. The time period is:

G1 Physics · Accepted Answer

For SHM, v₁²=ω²(A²−x₁²) and v₂²=ω²(A²−x₂²). Subtract: v₁²−v₂²=ω²(x₂²−x₁²). Thus ω²=(v₁²−v₂²)/(x₂²−x₁²), and T=2π/ω=2π√[(x₂²−x₁²)/(v₁²−v₂²)]. Correct option: 4.