 Perforated-disc pendulum

For a plane lamina suspended at O, treat removed pieces as negative masses and attached pieces as positive ones. Add their moments of inertia about O using the parallel axis theorem, and add their first moments to locate the centre of mass. If the first moments lie along one axis, the gravitational restoring coefficient is $g|{\sum }_i{m}_i{x}_i|$. Dividing it by the total inertia gives the small-oscillation angular frequency squared. Both the restoring moment and inertia change when material is moved.