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Help with a SDOF system, spring and base?

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data
    f2sxQnk.jpg


    2. Relevant equations
    Maybe the step response equation?
    XIVzJAw.gif


    3. The attempt at a solution
    I don't really understand the difference between a and b, but he said part a was supposed to be quite easy. Is a just:
    mx'' = -k(x-y) - c(x' - y')
    or something along those lines? where x represents the displacement of the seat, and y the displacement of the base, so y' = 4cm? or y = 4cm?

    Using F0= k * 0.04, and plugging the values into the step response equation, with zeta = c/2m*ωn, and ωn = √ (k/m), and ωd= √(1-ζ2n, I got the graph at the bottom (I think), which makes me assume it's right, without much idea what I put for b. When it says 'develop', does this mean derive the step-response equation? Or just plug in the variables?

    Any help would be appreciated. Thank you
     
  2. jcsd
  3. Mar 11, 2014 #2

    rude man

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    Looks like you have the right equation for part a.

    For part b you should input a step into y(t) at t=0 and solve the diff. equation for x(t). I would use the Laplace transform if you're familiar with it, otherwise you'd have to grind out the classical diff. eq.

    I don't know if your "step response equation" is correct. It looks plausible. I would start from scratch rather than use it unless you get a strong indication that that's what's expected of you. What would you do with the tau in it?
     
  4. Mar 11, 2014 #3
    oh sorry, (t - tau) would just be t, taking tau=o as the moment that it steps
     
    Last edited: Mar 11, 2014
  5. Mar 11, 2014 #4

    rude man

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    OK, so how about F0? You don't know what that value is ...

    Again, I suggest working with your part a equation.
    I would let x=0 and y=0 when t<0.
     
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