Michael and I are interested in the behaviour of individual pendulum swings where averaging hides useful detail. The easiest way (I think) is to compare the test pendulum with a much more accurate clock, and the more accurate the better.
With a pendulum clock, tens of microseconds are interesting, and picosecond resolution would be even more revealing. It's a bit like measuring length: to measure a thou accurately, you need an instrument that can get close to tenths.
Looking closely at the timing of a pendulum shows clock faults, for example I think I can detect the difference between a pendulum swinging true and one following an ellipse. On my test rig an elliptical swing has more jitter, I'm not sure why. I suspect it's due to a combination of the impulse being misplaced relative to the bob, torsion in the rod, and maybe bending at the pivot.
Dave
The PICTIC I linked to (corrupted by smiley) "http://www.ko4bb.com/doku2015/doku.php?id=precision_timing
ictic" Google KO4BB (O not zero) pictic to find it
is ideal for what you want. run it from a 10MHz OCXO and a optocoupler obscured every pendulum swing and it will send the time of every swing to a PC via the serial port.
Robert G8RPI.