ABSTRACT

Every atom may behave as an oscillator, vibrating about an equilibrium position. If one mass is pulled aside, as shown, and then released, the motion is quickly transferred to the other mass through a typical superposition of normal modes. A real physical system, however, is usually capable of vibrating in many different ways, and may produce too many different frequencies—like a sort of grand piano. A simple example is a flexible chain suspended from one end. It is found that there is a whole succession of frequencies at which every point on the chain vibrates in simple harmonic motion at the same frequency, so that the shape of the chain remains constant in the sense that the displacements of the various parts always preserve fixed ratios. Every atom may behave as an oscillator, vibrating about an equilibrium position. But the motion of each atom affects its neighbors so that, in effect, all the atoms of the solid are coupled together.