Halliday, Resnick & Walker — Oscillations: Problem Problem_48

A rectangular block, with face lengths \(a = 35\text{ cm}\) and \(b = 45\text{ cm}\), 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 15.26 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?