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Static displacement of a spring

  1. Oct 8, 2014 #1
    1. The problem statement, all variables and given/known data
    How would I find the static displacement of a spring due to maximum applied force? I asking this for arbitrary equation say ##m\ddot{x} + kx = F(t)##.

    2. Relevant equations
    Hooke's law

    3. The attempt at a solution
    I don't know how one would do this. Would it be find the maximum force and then use Hooke's law?
     
  2. jcsd
  3. Oct 8, 2014 #2
    Do you have an actual problem in mind?
    If it's "static" why do you have a time dependent force?
     
  4. Oct 8, 2014 #3
    That is the type of equation of motion I have and the question is what is the static displacement due to the maximum force applied. I know ##k##, ##m##, and ##F(t)## but I looking for an explanation on how I would find this.
     
  5. Oct 8, 2014 #4

    Orodruin

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    If the force depends on t, then x is not static ...
     
  6. Oct 8, 2014 #5
    This is a second question form the other question you answered. That is the exact verbiage of the question and you saw the problem statement and ##x(t)## solution.
     
  7. Oct 8, 2014 #6

    Orodruin

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    I am pretty sure this is your interpretation of the problem due to how you phrased it, but it is not coming through so all I can offer is my interpretation of your interpretation, namely: What would be the static displacement if the force was constant and equal to the maximal value of F(t)?

    Then yes, you would find the maximal value of F and plug it into Hooke's law due to force equilibrium at the static point. Alternatively, you would note that all time derivatives are zero for any static solution. Thus ##\ddot x=0## and you again get the same.
     
  8. Oct 8, 2014 #7
    I can take a picture of the question so you can see it is identical. I just added the how would I find.
     
  9. Oct 8, 2014 #8

    Orodruin

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    In that case, the only interpretation I can find that makes any sense is the one above. Some problem writers really need to learn to formulate better ...
     
  10. Oct 8, 2014 #9
    One more question, ##F_{\max} = \lvert F_{\max}\rvert##, correct? I think this must be the case since it is oscillating the max force could be in the reverse direction as well.
     
  11. Oct 8, 2014 #10
    Yes, this may be useful. Even if you reproduced verbatim part of the problem, you did not reproduce the text completely.
     
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