In simple harmonic motion, the total mechanical energy remains constant.

• A. increases
• B. remains constant
• C. decreases
• D. is zero

Answer: (B)

Total mechanical energy in undamped simple harmonic motion is conserved because the restoring force is conservative, so the work it does converts energy between potential and kinetic without any losses. At any instant, the energy is the sum of kinetic and potential: E = 1/2 m v^2 + 1/2 k x^2, and this total stays constant—equal to 1/2 k A^2 for the oscillation with amplitude A. At the extreme positions, velocity is zero and energy is all potential; at the equilibrium position, potential is zero and energy is all kinetic. In the ideal case, energy simply trades between these forms but never changes in amount. If damping were present or external work added, the total mechanical energy would alter, but for ideal simple harmonic motion it remains constant.