The question concerns classical mechanics and conservation of energy.
Imagine a piston in a cylinder, lying down so that the piston moves horizontally. The cylinder is open at both ends (no compression of a gas). For simplicity, lets assume no friction, no sound, no heat effects, no gravity, and that the system is isolated in a vacuum.
The piston has a connecting rod attached to a revolving flywheel. Consequently the piston oscillates back and forth within the cylinder. The motion of the piston resembles simple harmonic motion ; its kinetic energy occilates across time, between a maximum at the middle of the cylinder, to zero at either end of the cylinder.
For simple harmonic motion (e.g., a weight attached to a spring, and oscillating horizontally on a frictionless table top), it is well known that oscillation of kinetic energy of the weight is counterbalanced exactly by a coincident oscillation of potential energy (e.g., potential energy due to compression of a spring) in such a way that the total energy remains constant at all times:
K = E sin^2(wt)
P = E cos^2(wt)
K + P = E
Furthermore, such motion is indefinite (excluding friction, etc...).
The question is: for the system described above involving the piston, cylinder and flywheel, where does the kinetic energy "go" as the piston slows down towards its stationary point at the extremes of its cylinder? From whence does it return as the piston accellerates towards its maximum kinetic energy at the middle of the cylinder? How does conservation of energy work for this system? What are the energy/time equations for this system? Does the flywheel revolve indefinitely with constant angular momentum, or must it slow down somehow?