The scenario is a wrecking ball swinging back and forth. Example why the position at which half the balls energy is kinetic and half is potential, is not equal to half of the amplitude.
This scenario involves the concept of mechanical energy being transformed between kinetic energy (energy of motion) and potential energy (energy of position). When the wrecking ball is at its highest point in its swing, all of its energy is in the form of potential energy. As it swings down towards the lowest point, this potential energy is converted into kinetic energy.
At the midpoint of the swing, the wrecking ball has a combination of kinetic and potential energy. The potential energy at this point is equal to the initial potential energy at the highest point, while the kinetic energy is equal to the initial kinetic energy at the lowest point. Therefore, at the midpoint, half of the energy is potential and half is kinetic.
The position at which half the ball's energy is kinetic and half is potential is not equal to half of the amplitude because the energy distribution depends on the height of the swing. The potential energy of the wrecking ball is directly proportional to its height above the ground, while the kinetic energy is related to the speed of the swing. As a result, the exact position at which half of the energy is kinetic and half is potential will vary depending on the amplitude of the swing. It is not necessarily at the halfway point of the swing's amplitude.