In a horizontal cylinder with a piston performing simple harmonic motion, the amplitude of the piston is not equal to the displacement amplitude of the medium, which is air in the cylinder. The medium itself does not move in the same way as the piston; it only expands and contracts due to the piston's motion. The displacement of the medium refers to the changes in pressure and density rather than physical movement. Understanding this distinction is crucial for analyzing the dynamics within the cylinder. The discussion clarifies the relationship between the piston's motion and the behavior of the medium.