Energy lost equals change in mechanical energy due to damping

Steps:

• Equilibrium stretch δ = 0.02 m, so spring constant k = weight / δ = 8 N / 0.02 m = 400 N/m.
• Set gravitational PE = 0 at X; initial energy = 0 J (unstretched spring, at rest).
• At final rest O: gravitational PE = -8 N × 0.02 m = -0.16 J; elastic PE = ½ k δ² = ½ × 400 × (0.02)² = 0.08 J; total = -0.08 J.
• Energy lost = initial total - final total = 0 J - (-0.08 J) = 0.08 J.

Why B is correct:

• B (0.08 J) equals the dissipated mechanical energy, per conservation of energy with damping.

Why the others are wrong:

• A: Underestimates by half, possibly from only spring PE at equilibrium.
• C: Equals gravitational PE drop to O, ignores spring PE gain.
• D: Equals gravitational PE drop to Y, irrelevant to final state.

Final answer: B