Although commonly sold in dollar stores and pound shops, these common solar powered rocking/flapping ornaments have a very interesting history.
It starts with electromechanical pendulum kickers that maintain constant swinging of a pendulum for timekeeping.
That evolved into compact electronic clocks that used the earliest transistors to keep a balance wheel rocking back and forth, before the high accuracy quartz clock appeared.
There have always been ornaments based on electronically pulsed pendulum technology, notably the kinetic art devices that were very popular in the 80's. They're still made and available on eBay.
The flappy leaf and rocker ornaments that use solar power have one extra trick. The ability to self start by pulsing the coil when the capacitor voltage reaches a threshold. They then self trigger from the magnetically induced current in the same coil to make the pendulum swing at its resonant frequency. The circuitry is so refined and cost-optimised that it has ended up as a COB blob-chip on a PCB with a capacitor, solar cell and coil.

Here's a good page to get you started on electronic pendulums:-
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Here's a Google search to find more pendulum circuits, projects and history:-
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