A Direct Treatment of the Foucault Pendulum

The equations of motion of the Foucault pendulum are set up in polar coordinates. The oscillation is shown to be simple harmonic for a particular angular velocity, −Ω sinφ, where Ω is the angular velocity of rotation of the earth and φ is the latitude. In general, the motion involves a constant areal velocity c and a nonlinear oscillation given by r+ω2r−c2/r3 = 0. This equation is integrated through the energy equation and shown to give the same precession as in the harmonic case.