University of Florida/Egm4313/s12 Report 2, Problem 2.6

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Problem 2.6[edit]

Solved by: Andrea Vargas

Problem Statement[edit]

For the following spring-dashpot-mass system (in series) find the values for the parameters knowing that the system has the double real root

Figure[edit]

R2.6.jpg

Solution[edit]

Previously, we have derived the following equation for such a system:
(From Sec 1 (d), (3) p.1-5)

We can write this equation in standard form by diving through by :

Here, we can take the coefficients of and as and :



Next,considering the double real root:

We can find the characteristic equation to be:

Which is in the form:


Then, we know that and :

Setting and from the first equation equal to these, we obtain:

                                                             



Clearly, there is an infinite amount of solutions to this problem because we have 2 equations but 3 unknowns. This can be solved by fixing one of the values and finding the other two.

Example of Solution[edit]

An example of fixing one of the constants to find the other two is provided here. By solving the simple equations above, we can illustrate how to find . We had:

If we fix the mass to . We find:



Then,



Finally, we obtain:

                                                             


--Andrea Vargas 21:44, 7 February 2012 (UTC)