Chaotic circuit for random number generation
Chua's circuit is a chaotic oscillator built from a RLC circuit and a nonlinear element. It's not simulating a double pendulum directly, but generates chaotically oscillating output.

If you're looking to generate hardware random numbers and aren't concerned about double pendulums specifically, there are easier ways. See wikipedia for examples. One famous but impractical technique was Silicon Graphics' random numbers generated from a lava lamp.

Intel's Ivy Bridge processors use metastable R-S latches to generate true randomness from thermal noise. So if you just want hardware random numbers, your computer may have them already.