Final answer:
This question addresses the concept of energy in a physics context, discussing potential energy, kinetic energy, and how these relate to the total energy line in the context of an oscillator. The total energy is represented as a constant line, and this constant value is divided between potential and kinetic energy, depending on the object's position in its motion.
Step-by-step explanation:
The question pertains to the energy of an oscillator, specifically concerning potential energy, kinetic energy, and the total energy of a system. At the turning points of an oscillator (±A), the speed is zero, implying that all the energy is in potential form, given by the equation E = k A²/2. The potential energy as a function of position x would plot as a parabola, intersecting with the total energy of the oscillator at these turning points. The kinetic energy is represented by the distance between this total energy line and the parabola.
An important aspect to note is that kinetic energy can never be negative, and hence, there exists a maximum potential and kinetic energy that the system can have based on the given total energy. Additionally, it must be understood that as an object is projected upwards, its kinetic energy decreases, and potential energy increases, contrary to the increase in kinetic energy as it falls back to the ground.