Finding the equation of a system involving dashpots and mass on wheels

  1. 1. The problem statement, all variables and given/known data
    consider the mechanical system below. Find the equation depicting the system. u is the input force. sorry for the poor picture, I had to draw it on my tablet...
    [​IMG]

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    2. Relevant equations
    F=ma


    3. The attempt at a solution
    I'm not sure how to treat the dashpot in parallel with the mass. I came up with the following system of equations:

    0=k1x+mx"+k2(x-y)+b(x-y)
    0=b(x-y)+k2(x-y)+k3(y-u)
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

  4. hi!
    oops I mistyped...
    0=k1x+mx"+k2(x-y)+b(x'-y')
    0=b(x'-y')+k2(x-y)+k3(y-u)
     
  5. I can't tell you anything for sure since I haven't done these problems in years. The way I used to check out the mechanical "circuit" when I got overwhelmed was based on my electrical knowledge. Your dashpot is a resistor and your mass is an inductor. Always use this as a double check when you're unsure of a mechanical setup. The info for the electrical setup will always be more easy to find.

    EDIT: Looking at your equations of motion now though, I think you have it or are close. There is no need to fudge with the circuit. Just find X and Y based on input u.
     
    Last edited: Jun 5, 2011
  6. 0=k1x+mx"+k2(x-y)+b(x'-y')
    0=b(y'-y')+k2(y-x)+k3*y+u

    after some more modification, but i'm still unsure...
     
  7. For starters:

    Note that u would be a velocity input, not a force input.

    b is by' - it has no contact with the velocity at x

    and I think for m it is m(y"-x")

    I haven't checked your eqautions yet, so patience please
     
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