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Simple harmonic motion problem involving matrices

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data
    2 equal masses are joined together by a spring of stiffness k. each of the masses is then connected to a wall with an identical spring. derive the equations of motion in matrix form. (a diagam has 2 masses with x1 on top of the first mass and x2 on top of the second.)


    2. Relevant equations
    hooke's law: F = kx


    3. The attempt at a solution
    mass 1:

    mx1'' = F(x2 - x1) - Fx1
    mx2'' = Fx2 - F(x2 - x1)

    ^ are these correct?
     
  2. jcsd
  3. Mar 30, 2009 #2
    Mass one looks good but mass two is off. What happened to your third spring ?
     
  4. Mar 30, 2009 #3
    Also, draw yourself a free body diagram.
     
  5. Mar 30, 2009 #4
    i did. there are only 2 displacements (x1 and x2), right? the extension of the third spring is not kx2?
     
  6. Mar 30, 2009 #5
    There are only two equations, but you need to include the third spring. If the masses are going to move springs 1,2, and 3 have to move with them.
     
  7. Mar 30, 2009 #6
    but each mass is connected to 2 springs. therefore each equation should only have 2 terms. the only mistake i can see with the second equation is that Fx2 (force from the THIRD spring) should be negative. oh, and sorry if i haven't been clear enough -- the diagram goes like this:

    [wall] [spring] [mass 1] [spring] [mass 2] [spring] [wall]
     
    Last edited: Mar 30, 2009
  8. Mar 30, 2009 #7
    Mass one depends upon springs 1 and 2. Mass two depends on springs 2 and 3. Rewrite your equations and redraw your FOB.
     
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