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

Problem 2.6

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Solved by: Andrea Vargas

Problem Statement

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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

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Solution

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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

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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)