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 sin (ω t + Φ) . A = 3 m, ω = 2 s⁻¹, Φ = (π/6) . At t = 0.5 : 2 × 0.5 + (π/6) = 1 + (π/6) = (π/3) + (π/6) = (π/2) . v = -2 × 3 sin ((π/2)) = -6 × 1 = -6 m/s . Applying x = A cos(ωt