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On my desk at the moment I have a pendulum maintained by a R-Pi PicoW using just a single coil and probably a few hundred thousand transistors (not counting the two external to the Pi!), but on the other hand it has some additional functions, such as measuring and controlling the pendulum amplitude, deriving drive pulses for the dial with some trickery to allow rating the clock, and potential for remote setting over Bluetooth/WiFi.
Probably many more than a few hundred thousand transistors in a PicoW, but couldn’t find out this morning. The number of transistors in a device used to be a selling point:

Five transistors, wow!!! Now even ordinary devices contain so many, the number has become meaningless. Ten years ago, the Intel i7 chip featured nearly 2 billion transistors, and things have moved on since then. Thirty years ago a computer transistor would have been a few hundred nanometres across. Today, the best is about 3nm, though the measure is so heavily polluted by sales-speak, that the actual transistor might be considerably bigger.
A pendulum can be pulsed electromagnetically with only one transistor, though two are better, or an NE555, or a few logic chips. Tempting to conclude the electronics are so simple there’s no point in using a microcontroller. Not so, because programmable devices have many advantages.
They can be reprogrammed to add and refine functions. And, they often replace a mass of conventional circuitry. Most microcontrollers come with a built-in peripherals that further reduce the need for external components. As a basic microcontroller is cheaper than an NE555, it’s become a general rule of thumb that anything that can be done with a microcontroller should be. Of course, they can’t do everything, but if a microcontroller is too slow, alternatives like the Field Gate Programmable Array also reduce the need for conventional components. And not just electronic parts – in a clock, intrusive mechanical features like the escapement and gear-train can also be eliminated. Electronic counters are frictionless, and the actual period doesn’t matter because it and rate are corrected in software, not by fiddling with the hardware.
My clock does does much the same as John’s PicoW with a distinctly less capable Arduino. It also measures temperature and air pressure, and logs them together with microsecond accurate period. Microsecond accuracy is assured by feeding the Arduino 1 second pulses from a GPS. (The clock is designed to run in two modes: first, by comparison with GPS, data is logged for several months and then analysed to extract calibration parameters; second, the program having been temp and pressure calibrated and tuned to swing the pendulum with least disturbance, the GPS is disconnected, and the clock keeps time with the pendulum. )
Being programmable opens the door to experimentation. For example, the strength of the impulse, when in the swing it’s applied, and how often it’s applied can all be programmed. On my clock, I confirmed, as expected, that it’s best to apply the impulse at bottom dead centre. Less expected, applying a light impulse on every stroke disturbed my pendulum less than applying a stronger impulse every ‘n’ strokes and then letting the pendulum swing free for many strokes. Ditto, only impulsing the pendulum when it falls below a certain amplitude proved more disturbing than applying a light impulse on every beat.
There’s a lot left undone, for example, programming the Arduino to tune impulses for best results automatically.
John could easily add these features if he needed them. And more! A picoW could easily manage several pendula, and average them.
The device demonstrated in Michael’s video link is most odd. Rocking a smart phone to fabricate evidence exercise has been taken is bonkers! Keeping an unused autowinding wristwatch going by rocking it would make more sense.
Dave