Trajectories of two-dimensional harmonic oscillators in a rotating frame: application to Foucault pendulum problem

The motion of a classical point particle submitted to a central restoring force in a rotating frame is studied. Trajectories taking account all fictitious forces are presented. The obtained solutions are applied to the problems of pendulums oscillating on the surface of the Earth, in particular regarding the Foucault pendulum. This makes it possible to obtain precise solutions and to characterize the trajectories as centered trochoid curves.