A pendulum is at rest with its bob pointing toward the center of the earth. The support of the pendulum is moved horizontally with uniform acceleration a, and the
pendulum starts to swing. Neglect rotation of the earth. Consider the motion of the pendulum as the pivot moves over a small distance d subtending an angle θ0 ≈ d/Re ≪
1 at the center of the earth. Show that if the period of the pendulum is 2π, the pendulum will continue to point toward the center of the earth, if effects of order
θ02 and higher are neglected.
