University of Florida/Egm4313/s12 Report 2, Problem 2.6
Problem 2.6
editSolved by: Andrea Vargas
Problem Statement
editFor the following spring-dashpot-mass system (in series) find the values for the parameters knowing that the system has the double real root
Figure
editSolution
editPreviously, 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
editAn 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)