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[Phys-l] An interesting driven parametrically coupled pendula

During my recent antique peregrinations I found a clock driven physical pendulum. Horologists define it as a compound pendulum, as it has two well defined bobs at the ends of a rod. Such a pendulum is common when a long period (beat) is required in a small space, e.g. tower clocks and metronomes. Such are driven by a usual escapement probably w/ a crutch. I'm not familiar w/ such clocks. This one was driven by moving the center of mass in the upper bob. It contained a small pendulum clock! It necessarily required a compound pendulum. The upper clock containing bob was immediately above the knife edge the lower bob was v. ~ 50 cm below the knife edge resulting in a period > 1.4 s.

Since pendula have interested me, I have rather exhaustively searched the subject and not found the analysis of such. Of course parametric driving is common, e.g. pumping a swing and varying the rod length (e.g. O Botafumeiro), but not coupling two pendulua in such a manner.

I examined the rod below the knife edge carefully and note the adjustment is in the form a two or three metal rods temperature compensator.

Any comments?