University of Florida/Egm4313/s12 Report 2, Problem 2.6
Problem 2.6[edit | edit source]
Solved by: Andrea Vargas
Problem Statement[edit | edit source]
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 | edit source]
Solution[edit | edit source]
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 | edit source]
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)