A conical pendulum has string length l and the string makes an angle θ with the vertical. Its time period is:
Options

Question

A conical pendulum has string length l and the string makes an angle θ with the vertical. Its time period is:

G1 Physics · Accepted Answer

Let the string tension be T. Vertical balance gives T cosθ = mg. Horizontal component supplies centripetal force: T sinθ = mω²(l sinθ). For sinθ≠0, T = mω²l. Combining with T cosθ=mg gives mω²l cosθ=mg, so ω² = g/(l cosθ). Hence the time period τ = 2π/ω = 2π√(l cosθ/g).