University of Florida/Eml4507/s13.team3.GuzyR3

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Problem 2: Dampened and Undamped System

On my honor, I have neither given nor received unauthorized aid in doing this assignment.

Given[edit]

Spring-damper-body arrangement for R3.2 [1]

Spring-damper-body arrangement as shown. Two separate forces applied to masses.








Find[edit]

1.Draw the FBDs of all components in the spring-mass-damper system on p.53-13, with the known disp dofs being at the left and right supports:


2. Derive (1) p.53-12, and (1)-(3) p. 53-13.

Solution[edit]

Free Body Diagrams (Question 1)[edit]

Dampened:Spring-damper-body free body
Undamped:Spring-body free body

The free body diagrams for a dampened system and undamped system can be seen to the right.

Solving the System (Question 2)[edit]

DAMPENED[edit]

Analyzing the forces on mass one, we obtain:

Analyzing the forces on mass two, we obtain:


Plugging equations into matrix form we obtain:

\

Notice how this form matches each matrix given in the problem statement. Plugging in the original yields and proves the following equation of motion for an undamped system:


UNDAMPED[edit]

Analyzing the forces on mass one, we obtain:

Analyzing the forces on mass two, we obtain:

Plugging equations into matrix form we obtain:

\

Notice how this form matches each matrix given in the problem statement. Plugging in the original yields and proves the following equation of motion for an undamped system: