Bill,
The simple version I mentioned doesn't really have any electronics. The mechanics takes care of the electronics. See the picture: when you close the circuit with S1, the electromagnet pulls the steel strip which immediately opens the electric circuit (S2) and disables the electromagnet, allowing the steel strip to spring back and close the circuit again, and so on...
It hard to predict the frequency with this design though, depends on the coil inductance and the core iron bar, as well as the steel strip. But it's easy enough to make and experiment.
Then, as I said, you can use a simple electronic circuit (based on a 555 IC or the like) to control the ON and OFF time intervals and frequency of the electromagnet power.
Daniel