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. Maximum acceleration: aₘₐₓ = ω² A . A = 7 m, ω = 5 s⁻¹ . aₘₐₓ = 5² × 7 = 25 × 7 = 175 m/s² . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 175 m/s² follows, reflecting SHM dependence on amplitude A, ω and system parameters.