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Homework Statement
Write equations that could be used to solve for, [tex]V_{1}(s) \quad , \quad V_{2}(s)[/tex] in the Laplace domain for the mechanical system shown in the figure attached.
Homework Equations
The Attempt at a Solution
I think I understand most of the problem, but I think I am confused about the direction of the forces.
I am looking to write two equations as follows,
[tex]\sum \text{Forces on M1} = 0 \quad , \quad \sum \text{Forces on M2} = 0 [/tex]
First,
[tex]\sum \text{Forces on M1} = 0[/tex]
[tex]b_{2}(v_{1}(t)  0) + b_{1}(v_{1}(t)  v_{2}(t)) + M_{1}\frac{dv_{1}(t)}{dt} = r(t)[/tex]
Second,
[tex]\sum \text{Forces on M2} = 0[/tex]
[tex]b_{1}(v_{2}(t)  v_{1}(t)) + k\int v_{2}(t) dt + M_{2}\frac{dv_{2}(t)}{dt} = 0[/tex]
Here are the things I am confused about,
 For the forces on the dampers, how do I figure out whether it is (v2v1) or (v1v2) in each of the two cases?
 Why is the force from the spring not considered in the first equation, i.e. summation of forces on M1?
I am capable of completing the rest of the problem without any issues, but I just want to clarify my understanding with regards to those two questions.
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