At which point in its swing does a pendulum have equal amounts of potential and kinetic energy?

The pendulum swing is a classic example of the conversion between potential and kinetic energy. As the pendulum moves, it exchanges energy between these two forms.

At the highest points of its swing, the pendulum has maximum potential energy and minimal kinetic energy because it is momentarily at rest before changing direction. Conversely, at the lowest point of the swing, all the energy is kinetic; the pendulum is moving at its maximum speed.

The point at which the pendulum has equal amounts of potential and kinetic energy occurs halfway through its swing. At this position, the pendulum has descended from its maximum height, where potential energy was the greatest, allowing some potential energy to convert to kinetic energy as it gains speed. However, it has not reached the lowest point yet, where kinetic energy peaks. Thus, at this halfway point, energy is balanced, leading to equal measures of both potential and kinetic energy.

This understanding highlights the pendulum's energy dynamics, demonstrating how energy transformation is a key principle in mechanics.