[This was a 4 part question. The first 2 parts were correctly done (so I didn't show much work for them). I'm not sure about the last 2 parts. I only need help with the last 2 parts.] 1. The problem statement, all variables and given/known data A closed hollow cylinder of length L = 0.5 m, cross sectional area A= 0.0004 m^2 and a negligible mass has a lead weight of mass m=0.1 kg inside at the bottom so that it floats vertically when placed in water. [1st part] Determine the distance, d, from the bottom of the cylinder to the surface of the water. I calculated d = 0.25m [2nd part] The cylinder is now pushed down a distance x from the equilibrium position, d, determined above. What is the additional force on the cylinder trying to restore it to its equilibrium position? I calculated F = 3.924x [3rd part] What is the period of the vertical oscillations of the cylinder? [4th part] Estimate the period of rotational oscillations, where the axis of the cylinder oscillates back and forth in a vertical plane. 2. Relevant equations [For part 1] (.1kg mass) = (mass of displaced water) = (density of water)(volume of submersed part of cylinder) [For part 2] (.1 kg + F) = (new displaced volume of water)(density of water) [For part 3] w = (k/m)^(1/2) T = (2pi)/w [For part 4] (torque) = -k(theta) w = (k/I)^(1/2) T = 2pi/w 3. The attempt at a solution [Part 3] T = 2pi/w = 2pi(m/k)^(1/2) = 2pi(.1/3.924)^(1/2) = 1.00303 seconds [?] [Part 4] T = 2pi/w = 2pi/ 25.0567 = 0.250758 seconds [?] Are these answers correct? Thanks.