How does a balance spring keep itself wound, or does it?
From what I understand, the balance spring is a torsional spring with very low loss which, together with the balance wheel, forms an underdamped mass-spring system. It does lose a tiny bit of energy with each oscillation cycle, but that is replenished by the energy stored in the main spring — this energy is transferred via the arm of the escapement, which is acted on by gears that are eventually coupled to the main spring.
