A grandfather clock uses a pendulum to measure time. A model of this pendulum is constructed as follows: One end of a rod of lengthl = 1.0m and mass mrod = 0.65kg is connected to a bearing (assume friction-less) and the other end connects to a solid cylinder of radius R = 0.12m. Part a) You wish to find the mass of the cylinder such that the period of oscillation is T = 2s. First find the moment of inertia of the rod and disk, and then calculate the center c mass distance. Finally use the period of oscillation of a physical pendulum to find the mass of the disk. Part b) Write down the equation of motion of the cylinder 0(t), assuming the angle of release is small (sin(0) = 0). Part c) Find the maximum tangential velocity of the swinging pendulum.

A grandfather clock uses a pendulum to measure time. A model of this pendulum is constructed as follows: One end of a rod of lengthl = 1.0m and mass mrod = 0.65kg is connected to a bearing (assume friction-less) and the other end connects to a solid cylinder of radius R = 0.12m. Part a) You wish to find the mass of the cylinder such that the period of oscillation is T = 2s. First find the moment of inertia of the rod and disk, and then calculate the center c mass distance. Finally use the period of oscillation of a physical pendulum to find the mass of the disk. Part b) Write down the equation of motion of the cylinder 0(t), assuming the angle of release is small (sin(0) = 0). Part c) Find the maximum tangential velocity of the swinging pendulum.