How do analog clocks/watches tick at exactly a second?
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They have some kind of [escapement gear](https://upload.wikimedia.org/wikipedia/commons/2/29/Anchor_escapement_animation_217x328px.gif). You can see from that gif that as the gear turns there is an arm (called the *pallet*) that catches the gear teeth so that the gear cannot continue rotating. A gear causes the pallet to oscillate back and forth and as it does so, it frees the gear to move *one* tooth before swinging back into place and stopping the gear.
A spring keeps constant tension on the gear so that it always wants to rotate, as soon as the pallet is out of the way. In [this gif](https://i.imgur.com/Wzdjaby.gif) you can see the spring twisting back and forth on the mechanism to oscillate the pallet. The pressure from the rotating escapement gear imparts energy back into the controller spring to keep it oscillating. That energy comes from the mainspring, which is the spring that you have to wind to keep the watch working (or else the watch is powered with a tiny electric motor). A wall clock might use a spring, an electric motor, or counterweights that are pulled by gravity. As the counterweights fall, they pull on a gear that powers the whole thing.
Instead of a controller spring, a clock may use a pendulum. A quirk of pendulums is that how far you lift them up doesn’t change how quickly they oscillate. Only the length and weight of the pendulum changes its period. Like the controller spring, as long as the period of the pendulum is known, then it can be used to control a pallet that controls an escapement gear which can be tuned with ratios to turn the hands at the right time.
The size and tension of the controller spring, along with the size and weight of the flywheel attached to it, control how quickly the pallet oscillates. Precise gear ratios connect the escapement gear to other gears which ultimately control the hands on the watch or clock. As long as the pallet is oscillating at a regular, predictable rate, the gears can be tuned with the ratios to turn at more or less exactly one second (and minute, and hour).
The precision of the size of the gears determines how accurate the clock or watch will be. And, as the energy source runs out – either the spring needs to be wound, the counterweights lifted, or the battery replaced, it doesn’t add as much energy back into the controller spring and it will inevitably slow down, making the mechanism less accurate.
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