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Springs and masses connected together in a line

  1. Jul 1, 2012 #1
    1. The problem statement, all variables and given/known data

    So there are 4 masses in a line. They are connected by 3 springs between them, denoted by k_12 & l_12 (spring coefficient + natural extension length), k_23 & l_23, etc.

    2. Relevant equations

    Write down the f = ma equations of motion for all 4 masses.

    3. The attempt at a solution

    See my image.



    This problem really annoys me because I always learn how to do it for the test but never remember. I think I've gone through 3 courses where this problem came up and every time I could never remember. Well now it's just a random exercise in a linear algebra text I'm reading and I wouldn't mind learning it right once and for all. After all I'm supposed to be an engineer.

    Thank you for any help.
     

    Attached Files:

  2. jcsd
  3. Jul 3, 2012 #2

    Simon Bridge

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    Well do you really need to memorize the problem? Besides, the time you do, someone will give you one with 5 or 3 masses, or springs with varying k :)

    It's like this one only with four masses instead of two. (You could use the Hamiltonian or Lagrangian mechanics of course.)
     
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