Final answer:
The kinetic energy of a mass-spring system with gravity is maximum when the mass passes through the equilibrium point of the spring where all potential energy is converted into kinetic energy.
Step-by-step explanation:
When considering a mass-spring system with gravity included, the kinetic energy (KE) will be a maximum when all the potential energy is converted into kinetic energy. This would occur when the mass passes through the equilibrium point of the spring, which is the point where the spring is neither stretched nor compressed.
In such a system, the total energy is conserved and is the sum of the kinetic, elastic potential, and gravitational potential energies. At the highest and lowest points in the motion, the kinetic energy is zero and the potential energy is at a maximum. As the mass moves through the equilibrium point of the spring, the gravitational potential energy and the elastic potential energy are minimum, allowing the maximum amount of total energy to be present as kinetic energy.
It's important to remember that the total energy of the system remains constant if there are no external forces doing work on the system, such as air resistance or friction. This principle falls under the conservation of mechanical energy theorem.