The discussion focuses on calculating the spring constant of compressed air in pneumatic springs, emphasizing that the relationship between pressure, volume, and temperature is governed by Boyle's law. As volume decreases, pressure increases, leading to a non-constant force response that deviates from Hooke's Law. The force required to compress the air can be estimated using the bulk modulus, with the formula linking pressure change to volume change. The derived elastic constant for the cylinder is influenced by both the material properties and the geometry of the system. Overall, understanding these relationships allows for predicting the force needed for specific displacements in pneumatic applications.