Question: 1. A pendulum is made from a thin homogeneous metal plate cut into an equilateral triangle. What is the frequency of small oscillations if the plate is suspended by one vertex? What is the frequency for the same plate suspended at a midpoint of one of the edges? For both cases assume that the oscillation is in the plane of the plate.
2. A uniform cube of side length a and density ? is suspended by one of its vertices. What is the frequency of small oscillations? What be the length of the equivalent ideal pendulum?
3. A reversible (Kater's) pendulum is one that when pivoted about either of two points has the same period for small oscillations. The pivot points are at un-equal distances b1 and b2 on opposite sides of the center of mass. What is the length of an ideal pendulum that has the same period? What advantage would such a reversible pendulum have over a physical pendulum with a single pivot point?