"Hello, world" is trivial. But what is the "FizzBuzz" question for an analog computer? Calculate the velocity/acceleration of a failing object under gravity?
FPGAs aren't really analog. FizzBuzz is just a counting operation, so the analog equivalent is just a pair of accumulators that discharges to a "Fizz" or "Buzz" led or perhaps a plotter arm if you wanted to print the whole list.