B. The restoring force on the pendulum ball is the component of gravity along the tangent direction of the arc, and the resultant force of the other component of gravity and the pull of the cycloid on the pendulum ball provides centripetal force. Only at the maximum displacement, the velocity is zero, the centripetal force is zero, the other component of gravity is balanced with the tension of the cycloid on the pendulum ball, and other positions are unbalanced. So, B is wrong.
C. When the pendulum ball passes through the equilibrium position, the restoring force is zero. Because the pendulum moves in a circle and passes through the equilibrium position, the resultant force is not zero, and the resultant force provides centripetal force, and the direction points to the suspension point. So, C is wrong.
D. The restoring force on the pendulum ball is the component of gravity along the tangent direction, and the resultant force of another component of gravity and the pulling force of the cycloid on the pendulum ball provides centripetal force and points to the suspension point. According to Newton's second law, the centripetal acceleration of the pendulum ball is zero at the maximum displacement, and the other component of gravity is equal to the pulling force of the cycloid on the pendulum ball. At other positions, another component of gravity is less than the pull of the cycloid on the pendulum ball, so D is correct.
Therefore, choose: d.