Practice question

**Sinusoidal description** links amplitude A and angular frequency ω to instantaneous values. Given x(t) = A cos(ωt), max acceleration ω²A quantifies force requirement F_max = m ω²A, and velocity at arbitrary x is v = ±ω√(A² - x²) from energy conservation. Velocity: v = ω A cos (ω t + Φ) . A = 8 m, ω = 2π s⁻¹, Φ = -(π/3) . At t = 0.25 : 2π × 0.25 - (π/3) = (π/2) - (π/3) = (π/6) . v = 2π × 8 cos (π/6) = 16π × (√(3)/2) ≈ 43.54 m/s . Applying x = A cos(ωt + φ), v =