- #1

- 1,097

- 3

## 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 (v2-v1) or (v1-v2) 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.