Analysis of Bi and Trifilar Suspension Oscillations

Bi and Trifilar suspensions are used to determine the gyradii of solid objects about a vertical axis by measuring the suspension length spacing and period of yaw oscillation. Corrections for the vertical motion for the finite oscillation amplitude and for the finite mass of the suspension lines are given. The effect of a center of mass displaced from the symmetry axis is analysed. The precision of such measurements can be enhanced by measuring the ratio of the yaw and sway periods of oscillation. Furthermore the double pendulum oscillation of the bifilar suspension can be used to determine the gyradius about a horizontal axis as well as the vertical position of the center of mass.