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ohmaley

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## Homework Statement

1) Two cylinder can roll without sliding on a horizontal plan. they are connected throught the center by a spring of rigidity "k".

They both share the same radius "R" and mass "m". The left cylinder has its mass around the perimeter and the right cylinder's mass is spread uniformly.http://tinypic.com/r/16kpevc/7

a)Determine the free body diagram. Figure out the horizontal and rotational mouvements of each rolling bodies.

b) adding the cinematic equations (the Xi in function of the rotation angles θi), determine the differential equation system in x1 and x2.

c) Calculate both w and their associated modes.

## Homework Equations

sum Fx = m*agx

sum Mg = Jg*α (alpha)

Inertia momentum of the two cyclinders:

Jg=(M*R^2)/2 for mass spread uniformly

Jg=m*R^2 for mass around perimeter

## The Attempt at a Solution

I figured since there is no sliding -> X1=R* θ1 and X2=R" θ2.

m1*ag=-k(x1-x2)

m2*ag=k(x1-x2)with x(t) = Rcos(wt), "R" being the amplitude

i am not sure how to proceed about this problem.

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