A spring-mass system (m = 1 kg, k = 100 N/m, light damping) is driven by F = 2·cos(ωt) N. (a) Find its natural frequency. (b) At which driving frequency is the response largest? (c) What happens if driven at 50 Hz? Step 1: (a) f₀ = (1/2π)√(k/m) = (1/2π)√100 = 10/(2π) ≈ 1.59 Hz. Step 2: (b) Resonance occurs when the driving frequency matches f₀ ≈ 1.59 Hz — amplitude peaks there. Step 3: (c) At 50 Hz (far above f₀) the mass cannot follow the rapid forcing; the response is tiny. Answer: (a) ≈ 1.59 Hz, (b) ≈ 1.59 Hz driving frequency, (c) negligible response. Timing the pushes to the natural rhythm is everything.