1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

DE - mass-spring system

  1. Feb 23, 2008 #1
    (I had made a thread with a problem similar to this one, but it turned a bit messy after finding out the professor made some mistakes and the wording of his problem was awkward ... however, this is it)

    Problem:

    Differential equation governing a forced, mass-spring system:
    [tex]X\text{''}+4*X=0.04*\cos (\omega *t)[/tex]

    Spring constant = 4
    Mass = 1Kg
    Mass starts from rest, at equilibrium

    Find the range of [tex]\omega[/tex] in which the system doesn't break given that the spring breaks if stretched more than 0.06 m from the equilibrium position.


    Attempt:

    Equilibrium position = 2.45 m

    [tex]X(t) = \left(2.45-\frac{0.04}{4-\omega ^2}\right) \text{cos}(2*t)+\frac{0.04 *\text{cos}(t *\omega )}{4-\omega ^2}[/tex]

    So, now, how would I find all [tex]\omega[/tex] such that [tex]X(t) > 2.51 = 2.45 + 0.06[/tex] for all [tex]t[/tex]?
    Don't know of any exact way of calculating this. Used MATLAB to approximate the range of \omega's and it is ~ [tex]1.997379 < \omega < 2.303155[/tex]

    Thanks
     
    Last edited: Feb 23, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: DE - mass-spring system
Loading...