1. The problem statement, all variables and given/known data The problem is this: Find the angular frequency of the system in the figure when it's displaced at a small angle from equlibrium, given that ρ_0 < ρ_1. There is friction with the ground, so the motion is a rolling motion, without slipping. 2. Relevant equations I used the following equations, and got a wrong answer: f_s = friction m = mass of small cylinder M = mass of large cylinder x = linear displacement from equilibrium θ - angular displacement from equilibrium for linear forces (here the tag stands for d/dt): f_s = (m+M)x'' since it's a rolling motion: x = Rθ so: x'' = Rθ'' And the equation for the moments, from the center of the large cylinder (I think this is wrong): f_sR - mgsinθ*R/2 = Iθ'' also: m = (π ρ_1 R^2)/4 M = π ρ_0 R^2 - (π ρ_0 R^2)/4 I = π ρ_0 R^4 - (π ρ_0 R^4)/2 + (π ρ_1 R^4)/2 3. The attempt at a solution Using all the above equations and getting the ODE for x gives (unless I got the factors wrong): ω = (ρ_1/(10ρ_0 + 6ρ_1))*(g/R) This is not right - the right answer is: ω = (10(ρ_1 - ρ_0)/(7(ρ_1 + 31ρ_0))*(g/R) Which is of course a lot more sensible since there shouldn't be an oscillation for ρ_1 = ρ_0, and for ρ_1 < ρ_0 the model is wrong. So what's the right answer? And what am I doing wrong? Thanks, Lior BTW - why isn't the latex working?