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I've read through the excellent guide to how mechanical watches work by Ciechanowski, but it leaves some questions unanswered.

The main spring of the watch, when it loses energy, can of course be re-wound using the watch's crown, and the guide above explains in detail how that happens.

But the hairsping of the watch, the one that drives the balance wheel, must lose energy at some point as well through friction, with the balance wheel oscillations dying down as a result. How is energy restored to that spring, i.e. how is it re-wound?

On a related note, the guide above also shows that the balance wheel is stopped, through friction, by a special lever during the process of time adjustment. If the balance wheel is thus stopped at a particularly bad time (i.e. when it's exactly at its midpoint position), wouldn't all of the energy in the hairspring be dissipated when the balance wheel is stopped? How does it re-start once the watch is out of time adjustment mode?

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I enjoyed the detailed and beautifully animated diagrams you linked.

The source of energy to the balance wheel is the end of the fork that is pressured by the jewels acting intermittently by the scapement gears.

As soon as the balance wheel is released it will be accelerating by the force of the fork handle, either clockwise or anticlockwise.

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