Practice question

**Mass-spring dynamics** show T depends on mass and stiffness, independent of amplitude for ideal spring. Given T and m, k = 4π² m/T² extracted, and energy E = ½ k A² connects amplitude to total mechanical energy, illustrating isochronism. Total energy: E = (1/2) k A² . A = 0.05 m, k = 320 N/m . E = 0.5 × 320 × (0.05)² = 0.5 × 320 × 0.0025 = 0.4 J . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.4 J follows, reflecting SHM dependence on amplitude A, ω and system parameters.