The Coriolis effect and coupled oscillations in a rotating swings amusement ride

Rotating swings are found in many different versions in parks around the world. They are beautiful examples of the equivalence between gravitational and inertial mass: Empty swings and swings with heavy adults hang at the same angle to the vertical. However, sometimes you may notice empty swings moving in a different pattern in an outdoor ride, where wind can induce additional motion, sideways or back to front, in addition to any oscillations caused by a tilted carousel head. This paper focuses on oscillations for the simpler case of a non-tilting roof. Even for this case, the oscillating motion is found to be complicated by the Coriolis effect, which leads to a gyroscopic coupling between sideways oscillations and back-to-front oscillations. This coupling is illustrated for a few special cases.