Vibration Prob: Obtain mass and stiffness matrices of pictured system.

[get144]

Can anyone solve this?

I am able to solve multi degree of freedom systems however I am unsure how to integrate the cylinder m into this systems matrix, or even form a useful free body diagram for it.
Maybe something like M=I(Theta Double Dot)=rR₂-rR₁ or am I missing something simple about the reaction forces on the cylinder?

 

[Deleted member 4993]

Can anyone solve this?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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[get144]

I can sole multi degree of freedom systems however I am unsure as to how the cylinder affects this problem.
Does it cause a force on m₂, or can i just ignore it and solve the rest of the system?
Should the cylinder be added to the matrix for the system. Maybe something like Sum of M = IÖ (Imagine that is a Theta).

Any help getting started and setting up the system matrix would be great. Thanks in Advance.

 

[Deleted member 4993]

I can sole multi degree of freedom systems however I am unsure as to how the cylinder affects this problem.
Does it cause a force on m₂, or can i just ignore it and solve the rest of the system?
Should the cylinder be added to the matrix for the system. Maybe something like Sum of M = IÖ (Imagine that is a Theta).

Any help getting started and setting up the system matrix would be great. Thanks in Advance.

The cylinder is coupled to the system assuming that it rolls without slipping.

So if the block has speed v (= dx/dt) then the angular speed of the cylinder would be w = v/r