Final answer:
The total energy of a pendulum at the start and when it stops is the same, demonstrating the conservation of mechanical energy. This means potential and kinetic energy trade off during the pendulum's swing but the total energy remains unchanged without external losses.
Step-by-step explanation:
When comparing the total energy of a pendulum at the start (when it has been lifted and is about to be released) with the total energy when the pendulum stops at its highest point on either side of its swing, we notice that these amounts of energy are the same. This observation aligns with the conservation of mechanical energy, which states that in the absence of non-conservative forces such as friction and air resistance, the total mechanical energy of a system remains constant during its motion. At the highest points, the pendulum has maximum potential energy and no kinetic energy. Conversely, at the bottom of its swing, the potential energy is at its lowest, and the kinetic energy is at its maximum. The significance of this is that we can describe the motion of a pendulum and determine its speed at various points without solving complex differential equations by using energy conservation principles.