Final answer:
The motion of a pendulum involves changes in potential and kinetic energy. The potential energy is greatest at the highest point and least at the lowest point, while the kinetic energy is greatest at the lowest point and least at the highest point. The total mechanical energy of the pendulum remains constant throughout its motion.
Step-by-step explanation:
When a pendulum moves from its greatest to lowest height and back up again, its potential energy and kinetic energy change. At the highest point of the pendulum swing, the potential energy is at its maximum, while the kinetic energy is at its minimum. As the pendulum moves towards the lowest point, the potential energy decreases and the kinetic energy increases. At the lowest point, the potential energy is at its minimum, while the kinetic energy is at its maximum. As the pendulum moves back up towards the highest point, the potential energy increases and the kinetic energy decreases.
The total mechanical energy of the pendulum remains constant throughout its motion, as long as there are no external forces (like friction) acting on it. This is because the pendulum oscillates between potential energy and kinetic energy, but the total energy remains the same due to the conservation of mechanical energy.