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First Order Differential Equation Problem

  1. Oct 21, 2008 #1
    1. The problem statement, all variables and given/known data
    A 14 lb weight attached to the end of spring stretches it 4 in. Find the equation of motion if the weight is released from rest at a point 3 inches above equilibrium position


    2. Relevant equations
    F=kx
    mx''+kx=0


    3. The attempt at a solution

    ok I need some help just finding out what the k constant is. I know I use hooks Law F=kx, and F is mg=kx. Do i consideer equilibrium when nothing is attached to it, and that is y=0? Then what is the x considered in Hooks Law equation mg=kx , is it the distant its stretched from equilibrium position ?


    Thanks
     
  2. jcsd
  3. Oct 21, 2008 #2
    First, this is a undamped second order problem.

    I would consider equilibrium is when mg=kx.


     
  4. Oct 21, 2008 #3
    now what do u mean by equillibrium, is that when its unstretched and no wait? or the differecne between unstretrched and stretches in the middle in other words ?
     
  5. Oct 21, 2008 #4
    when the spring is stretched (downward) to x_0 such that kx_0=mg, it's equillibrium, that's y=0.

     
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