A 0.5-kg mass on a spring (k = 50 N/m) has damping constant b = 0.4 kg/s. Identify the damping regime and find how long the amplitude takes to fall to half. Step 1: Compare b² = 0.16 with 4mk = 4 × 0.5 × 50 = 100. Since 0.16 < 100, it is lightly (under) damped. Step 2: Amplitude decays as A₀e^(−bt/2m) = A₀e^(−0.4t). Half amplitude: e^(−0.4t) = 0.5 → t = ln2/0.4 ≈ 1.73 s. Answer: Underdamped; amplitude halves every ≈ 1.7 s. The mass still oscillates (period ≈ 2π√(m/k) ≈ 0.63 s), dying out over a few cycles.