Remember the Nikola Tesla Electric Oscillator?

Now if you know the period of oscillation, then you can use it to drive the mechanism of a watch.

The need to tell time at sea is what drove non pendulum based time keeping for mechanical watches.

In a mechanical clock, the pendulum from a grandfather clock is replaced with an oscillating mass in a spring.

A coiled string is used with a rotating mass. A coiled spring that repeatedly winds up.