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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Let’s look at a different clock works as all clocks operate under similar principles. You need 2 things first is a power source and the second is timing device. In grandfather clocks the power source is gravity pulling a weight down. The timing or regulated by a weighted pendulum which swings at a constant rate no matter how much force you apply to it. The rate at which a pendulum swings is called it’s “period” and period in a free hanging pendulum is only determined by the weight on the end and the distance of the weight from the pivot. It doesn’t matter how hard we push it because the farther it swings the faster it will return to the other side as gravity will accelerate it more, thus keeping the period the same as if we only pushed it a little
Now a watch works by replacing gravity with springs and the pendulum with a balance wheel. But the same still holds true. It doesn’t matter how hard the watch pushes on the balance wheel because the harder it pushes the more it will wind the balance spring (aka “hair spring”) the more the hair spring winds the harder it will swing back keeping the period of the balance roughly the same regardless of any variation on the force pushed to it.
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