For a vibrating string, these modes are called standing waves or harmonics.
In a form of analysis of macromolecules named for these things, a mass-weighted Hessian matrix of second-order derivatives of the potential energy is computed, then diagonalized, then its largest eigenvalues are found. Wilson's GF method involves transforming from internal coordinates to a set of coordinates based on these phenomena, and in general the system of coordinates in which each of these has its own equation of motion is the one in which the mass tensor and A-tensor are diagonal. In one simple system, these things can be found by transforming the coordinates of the system to the sum and difference of the displacements, and that system has two of these, one with omega equal to square root of quantity k plus 2 k prime over m and one with (*) omega equal to square root of k over m. In general, these things can be found by solving the secular determinant of a system of equations of motion. Any motion of a given system can be decomposed into a linear combination of these modes, and they occur at resonant frequencies. For a vibrating string, these modes are called standing waves or harmonics. For 10 points, name these modes of a system in which all parts oscillate sinusoidally with a fixed phase relation.
In a form of analysis of macromolecules named for these things, a mass-weighted Hessian matrix of second-order derivatives of the potential energy is computed, then diagonalized, then its largest eigenvalues are found.
normal modes [accept normal mode analysis; prompt on “resonant modes” or “resonance” or “resonance modes” or “natural frequencies” or “natural modes” or “eigenmodes” or “eigenfrequencies”]