J. Forster wrote:
The problem is straight forward, except for sensing the position of the
pendulum so the impulse is applied at the correct phase.

There must be a bunch of published designs, but if I were to try it, I'd
use something optical or capacitive.

For optical, I'd put a annular ring of IR LED/Phototransistor assemblies
around the center, wired OR the outputs, and use the signal to trigger the
impulse. The bottom of the pendulum should be polished or mirrored.



The usual scheme is a couple of optical paths at the top of the pendulum with lenses to focus the beam down to a very small diameter (smaller than the wire diameter). The two optical paths are at 90 degrees to each other, and are logically anded either by using a pair of detectors/paths, or by using a mirror to fold the path.

It's aligned with the pendulum perfectly stationary (i.e. it's been sitting still for a day or two) so the beam trigger occurs precisely at the center point.



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