Determine the equations of motions in terms of x and gamma.
Assume small angles and that the wheel rolls without slip. The mass of the thin homogeneous large disk
of radius 2R is 2m. The mass of the thin homogeneous inner disk of radius R is m. The rod of length 2R is massless and rigid. The two pulleys are massless.
I have attached my homework set and the problem is number 15. (I wouldn't be able to describe this very well)
We are supposed to use Newtons method.
See uploaded images for the answer and relevant equations.
The Attempt at a Solution
See other uploaded image for my attempt at the solution.
I'm confused as to what equations from what free body diagrams I should be using. Also, I don't know if the substitutions I am making or the constraints I have set up for the problem are right.
x_1 = R*theta ( displacements for wheels on top)
x_2 = x_1 - 2R*theta - 2R*gamma
F_s1 = k(x_1 + r*theta) (spring attached to wall)
F_s2 = T_1 = k(x_1 + r*theta) (spring between pulleys)
T_2 = mg
T_2x = T_2*gamma
F_friction = ?
I also summed moments about A which is where the smaller disk makes contact with the ground.
Any help on the matter would be greatly appreciated.