Final answer:
Total mechanical energy is conserved in a system where no non-conservative forces are acting. In the case of a rock falling with negligible air resistance, mechanical energy is conserved because there is no significant energy loss to friction or drag.
Step-by-step explanation:
The question "In which of the following systems is the total mechanical energy conserved?" relates to the conservation of mechanical energy in physics. Out of the given options, the correct one is D) A rock falling down from a height above the ground with negligible air resistance. This is because when air resistance is negligible, the system experiences no non-conservative forces like friction or drag, and thus the sum of kinetic and potential energy remains constant throughout the rock's fall. In the other options, energy is not conserved due to various reasons: A) Amplitude damping indicates energy loss through non-conservative forces, B) An inclined plane may have friction, even with constant speed, and C) A train coming to a stop is dissipating kinetic energy through non-conservative forces like friction.