Athin rod of length l rests on top of a half-cylinder of radius r as shown. the contact is highly frictional, so the rod can roll from its peak position but cannot slide (a) by considering slight rolling displacements, show that the horizontal orientation is one of 9. stable equilibrium, and find the period of small oscillations about this equilibrium. (b) physically interpret the limiting values of the period, i. e., for very small and very large values of r and l (c) (extra credit) make some measurements at home with simple objects like pencils, rulers, cans, etc., and compare your results with theory. you must include a photo of your apparatus, and you must have at least 8 unique combinations of r and l. (for example, you could use two different-sized cans like coke and red bull, with 4 different lengths of stick on each.) consider how to make the data taking as accurate as possible, and include this procedure in your writeup. don't worry if your data does not fit the theory well, but do speculate about why that may be