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Damping Force
A damping force is a force that sweeps energy away from an otherwise conservative system. Real oscillatory systems such as the damped pendulum are acted upon by at least one force that "damps," or steadily decreases, the amount of energy that was initially present at the start of the motion.
Air Resistance
For the case of the damped pendulum, air resistance is a non-conservative force that slows the motion. This force is a consequence of the pendulum's swing through the viscous medium of air. The air molecules, although very small and spread out, collide with the pendulum continually enough to sweep energy out of the system in the form of heat and sound.
Pulley Friction
When the string of the pendulum is attached to a pulley, friction arises. Friction is a non-conservative force that results in heat localized between two objects whose surfaces slide across one another. The energy required to generate the heat is energy that is swept out of the system of motion. The heat from friction dissipates into the surrounding environment as opposed to being recycled back into the system.