The arrangement shown in the figure is called trifiliar suspension. It consists of a circular disc of uniform thickness suspended from ceiling by means of three uniform wires of equal length. The points of suspension are equispaced from the centre of the disc. If a small angular displacement is given to the disc in its own plane and left, the disc oscillates in horizontal plane about the vertical axis passing through its centre. The equation of motion of the disc is given by,
J0 = mass moment of inertia of the disc about vertical axis passing through its center.
For the disc, J0 is given by where m0 is mass of the disc and r its radius.
=angular acceleration of the disc
a = distance between the point of suspension on the disc and its centre
l = length of wire between the point of suspension on the ceiling and the disc
Let an irregularly shaped solid body of mass m be kept on the disc with its centre of mass aligned with the vertical axis passing through the centre of the disc. And let the disc alongwith the body be set into angular oscillations as before. Then the equation of motion of the disc together with the solid body is given by,
The period of oscillation is given by