Practice question

**Simple pendulum** for small angles approximates SHM with period T = 2π√(L/g), frequency f = (1/2π)√(g/L), angular frequency ω = √(g/L) (rad/s), independent of mass. L length from pivot to centre of mass (m), g = 9.8 m/s² acceleration due to gravity, approximation sinθ ≈ θ (rad) for θ < 10°. Period: T = 2π √((L/g)) . T ∝ (1/√(g)) . (Tₚlₐₙₑt/TEₐrth) = √((gEₐrth/gₚlₐₙₑt)) = √((9.8/2.45)) = √(4) = 2 . Tₚlₐₙₑt = 2 × 3 = 6 s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 6 s