In the simplest mathemathical case, the aforementioned 'fat test' can be seen
as the setup of a simple gravity pendulum. Let us assume that the road is a
large half-pipe, aka a hollow hemisphere.
Each cyclist starts at a set angle on one side, and accelerates downwards
towards the lowest point by the act of gravity. After reaching this point,
inertia will carry the cyclists upwards along the other quadrant. The upwards
momentum is, by the same laws, counteracted by gravity, causing them to
accelerate in the opposite direction as they cross the threshold and begin to
move up the hemisphere.
The pendulum 'string' defines the actual length of the total hemisphere and
also represents the force on the wheels of the bicycle, preventing it from
simply falling into the road. This force acts perpendicularly to the current
position of the cyclist on the hemisphere.
In this situation, the laws of physics state that the actual mass of the 'bob'
or in this case, the cyclist does not affect the length of the swing (and the
time it takes for the cyclists to stop accelerating upwards and come back the
same way... the period).
Also, I think Galileo did an experiment involving two equally shaped objects
of different masses dropped from a large height yielding these results.
See:
http://en.wikipedia.org/wiki/Pendulum for more info.