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Displacements in springs

  1. Feb 27, 2016 #1
    1. The problem statement, all variables and given/known data
    A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is

    1423749846508Capture.PNG


    2. Relevant equations


    3. The attempt at a solution

    I don't really know how to do this, but here's what I know:
    From energy conservation, 1/2 k x2 + 1/2 (4k) x2 = 1/2 k y2 + 1/2 (4k) y2
    So, I get y=x.
    Which isn't the answer. The answer is (C).
    I don't understand why.
     
  2. jcsd
  3. Feb 27, 2016 #2

    SteamKing

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    What's (C) mean?
     
  4. Feb 27, 2016 #3
    Oh sorry, I meant the answer is 1/2
     
  5. Feb 28, 2016 #4
    Hint : Energy conservation is the correct method to use here. Application, though, is wrong.

    When you move B x to the right, consider M2 and B to be one system(Why?).
    Similarly, when B moves y to the left, consider M1 and B to be one system(Why?).

    The reasoning for this can be obtained from diagram II.

    Hope this helps,
    Qwertywerty.
     
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