Practice question

**Oscillation of mass attached to spring** follows Hooke's law F = -k x, SHM with ω = √(k/m). Effective stiffness for two identical springs in parallel doubles, k_eff = 2k, increasing frequency by √2, while series halves stiffness to k/2, lowering frequency. Energy E = ½ k_eff A². T = 2π √((m/k)) . 0.7 = 2π √((0.7/k)) ⇒ (0.7/2π) = √((0.7/k)) . (0.1114)² = (0.7/k) ⇒ k = (0.7/0.01241) ≈ 56.4 N/m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 56.4 N/m follows, reflecting SHM dependence on amplitude A, ω and system parameters.