When people talk about íperpetual motion machinesí they usually mean machines from which useful work can be extracted forever. That would violate the laws of thermodynamics.
What you mean is something that would just keep oscillating forever, without providing any work. Thatís still impossible.
In your example, if there were absolutely no air in contact with the pendulum, and if it had a perfectly frictionless pivot, you might wonder where its energy could go. Because it has a mass which keeps accelerating, it will radiate gravitational waves, and gradually lose energy and slow down.
OK, that will take a long time. But a process exactly like that happens with some astronomical objects, for which the slowing due to gravitational radiation is measured.
Quantum-mechanical systems in their lowest energy states (think atoms with electrons in their orbits) still have kinetic energy which never goes away, but also from which no energy can be extracted (there is no lower energy state than the lowest one). The electrons have energies, meaning that the average square
of the momentum of the electrons does not vanish. That's true even though at any time the average momentum is zero.
(republished on 07/13/06)