Practice question

**Velocity and acceleration in SHM** follow from differentiation, showing 90° phase lead of v over x and 180° for a over x. At mean position x=0, a=0, v=±ωA maximum; at extremes x=±A, v=0, a=∓ω²A maximum magnitude, illustrating energy conversion. Velocity: v = ω A cos (ω t + Φ) . A = 7 m, ω = 2 s⁻¹, Φ = (π/4) . At t = 0 : v = 2 × 7 cos (π/4) = 14 × (√(2)/2) = 7√(2) ≈ 9.9 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² =