Final answer:
The quantity that changes the most in a mass-and-spring oscillator due to damping as time passes is the amplitude of the oscillations, with energy being dissipated typically as thermal energy.
Step-by-step explanation:
A mass-and-spring oscillator experiencing damping due to friction will see the most change in its amplitude of oscillations over time. In a damped oscillator, the non-conservative damping forces, such as friction or viscosity, remove energy from the system, usually converting it into thermal energy. This can be observed as the gradual decrease in the amplitude of oscillations, while the period and frequency remain constant for systems with small damping. For very large damping, the system does not oscillate and instead slowly moves toward equilibrium.
When submerging such a system in a liquid like water, the external damping force exerted by the liquid against the motion inhibits the oscillations drastically, demonstrating the same decrease in mechanical energy of the system. The energy transformation here is from mechanical to thermal energy as the system is damped, which indicates the damping's effect on the energy conservation within the oscillator.
Overall, the existence of damping forces, whether from friction or viscosity, requires a continuous input of energy to maintain the oscillations, just as you would need to keep pumping a swing to counteract the dampening forces.