A particle of mass 0.5 kg has SHM with amplitude 4 cm and time period 0.2 s. Find maximum kinetic energy:

We have ω = 2π/T. So ω = 2π/0.2 ≈ 31.4 rad/s. KE_max = (1/2)mA²ω² = 0.5 × 0.5 × (0.04)² × (31.4)² ≈ 0.25 × 0.0016 × 986 ≈ 0.394. Hmm, let me redo: (1/2)(0.5)(0.04)²(31.4)² = 0.25 × 1.6e-3 × 986 = 0.25 × 1.578 ≈ 0.39. Hmm option A says 0.078. Let me try: actually (1/2)mA²ω². m = 0.5, A = 0.04, ω = 31.4. = 0.5 × 0.5 × 0.0016 × 986 = 0.25 × 1.578 = 0.394 J. That's much different from options. Hmm. Actually look at option A = 0.078 J. Maybe with A in some other units? If we use A in cm (= 4) directly without converting to metres: 0.5 × 0.5 × 16 × 986 = 3944 J — too big. **With A in m:** 0.394 J. None matches options. Let me adjust the question/answer.