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. T = 2π √((m/k)) . 0.5 = 2π √((0.5/k)) ⇒ (0.5/2π) = √((0.5/k)) . (0.0796)² = (0.5/k) ⇒ k = (0.5/0.00634) ≈ 78.9 N/m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 78.9 N/m follows, reflecting SHM dependence on amplitude A, ω and system parameters.