Vibration frequency response function can be calculated, thereby characterizing the system. This technique is used in the field of experimental modal analysis to determine the vibration characteristics of a structure. The simple mass–spring–damper model is the foundation of vibration analysis, but what about more complex systems? The mass–spring–damper model described above is called a single degree of freedom (SDOF) model since the mass is assumed to only move up and down. In more complex systems, the system must be discretized into more masses that move in more than one direction, adding degrees of freedom. The major concepts of multiple degrees of
Molecular vibration each of the four C-H bonds. Illustrations of symmetry-adapted coordinates for most small molecules can be found in Nakamoto. The normal coordinates, denoted as "Q", refer to the positions of atoms away from their equilibrium positions, with respect to a normal mode of vibration. Each normal mode is assigned a single normal coordinate, and so the normal coordinate refers to the "progress" along that normal mode at any given time. Formally, normal modes are determined by solving a secular determinant, and then the normal coordinates (over the normal modes) can be expressed as a summation over the cartesian coordinates (over