I know that mechanical watches have a spring that they wind to store energy, and un-winding the spring produces energy for the watch. But a spring produces a lot of force when it’s very tightly wound, and very little when it’s almost completely un-wound. So how does the watch even that out with high precision?
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There are plenty of great technical answers here, but how about an analogy? As others have pointed out, mechanical watches have a device inside that acts as a pendulum. Picture pushing a kid on a swing. The rate of swinging is the same whether you give the kid a gentle push or a more forceful one. As long as you’re pushing at all, the swing keeps swinging (at different heights maybe) at the same rate.
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