1. The problem statement, all variables and given/known data Here is the problem with my 3 attempts: 1. Alright, so the first attempt, I did not take into account the rotation of the cylinder ωc so I think it is wrong. But it seems to make sense because the whole cylinder rotates about O, so if I find that energy using parallel axis theorem it should get me the correct answer? 2. Here I said the energy from the cylinder is due to the rotational energy of the cylinder itself and also the velocity of the cylinder. I think this one is correct, what do you guys think? 3. I am not sure how to use moment to solve for the natural frequency. For some reason it gave me the same answer as 1. which I think is wrong. Is this one correct? I know this is a long question, but if anyone could give me some insight on whether or not I did it right, it would be greatly appreciated!