Practice question

**Conservation of mechanical energy** in undamped SHM implies total energy proportional to amplitude squared A² and spring constant k. E = ½ k A² allows amplitude determination from known E and k via A = √(2E/k), with k = m ω² linking dynamical and energetic descriptions for spring-mass system. Velocity: v = -ω A sin (ω t + Φ) . A = 4 m, ω = 3π s⁻¹, Φ = (π/6) . At t = 0 : v = -3π × 4 sin (π/6) = -12π × 0.5 ≈ -18.84 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ),