A Mechanical Analyzer for the Solution of Secular Equations and the Calculation of Molecular Vibration Frequencies

A set of coupled harmonic oscillators has been constructed, so designed that it can be used to solve the numerical secular equations occurring in the theory of the vibration of polyatomic molecules and in other problems. Each oscillator consists of a shaft with cross arms carrying weights to increase the moment of inertia and springs to provide restoring force. The unit is free to rotate about the axis of the shaft, except for the restoring force of the springs. The various units are connected to one another by additional springs. In operation the springs and weights are adjusted to values which represent the coefficients of the secular equation to be solved, the whole device is driven by an eccentric of variable speed, and the frequencies of resonance, representing the roots of the equation, are measured.