NOTES
The Ringworld navigation problem is like the Earth's, only turned on its side. Now some horizontal motion is stable, and some is not.
Motion in the "north/south" direction is just like motion along the earth's surface - the equivalent Earth-radius pendulum is much longer though, since the radius of curvature of the Ringworld surface in the north-south direction is an amazing 166 astronomical units, making the "Schuler" oscillation period about 11.5 days (if you include the effects previously mentioned that would increase the size of the central hump, the radius of curvature, and thus the oscillation period will decrease).
Motion in the "spinward" / "Antispinward" direction however is much different - now in effect, the pendulum is upside down, so errors in those directions will be unstable, doubling about once a day.
There still will be errors with the same period as the Ring's rotational period - in this case a period of about 9.4 days.