Final answer:
The centripetal force is greatest at the lowest point of a pendulum's swing, where the velocity is highest and corresponds to the equilibrium position in simple harmonic motion.
Step-by-step explanation:
When considering the motion of a pendulum and specifically looking at the centripetal force involved in its swinging motion, the centripetal force is greatest at the lowest point of the swing. At this point, the velocity of the pendulum bob is at its maximum, requiring a larger centripetal force to keep it moving in a circular path. In the context of simple harmonic motion, the lowest point is also referred to as the equilibrium position, which is where the pendulum bob would naturally rest if there were no forces acting upon it.