Halliday, Resnick & Walker — Oscillations: Problem 16

16 A rectangular block, with face lengths a = 35 cm and b = 45 cm, is to be suspended on a thin horizontal rod running through a narrow hole in the block. The block is then to be set swinging about the rod like a pendulum, through small angles so that it is in SHM. Figure 15-28 shows one possible position of the hole, at distance r from the block’s center, along a line connecting the center with a corner. (a) Plot the period versus distance r along that line such that the minimum in the curve is apparent. (b) For what value of r does that minimum occur? There is a line of points around the block’s center for which the period of swinging has the same minimum value. (c) What shape does that line make?