Lagrange equation for mass-spring-damper-pendulum

  1. Can someone kind of give me a step by step as to how you get the equations of motion for this problem?

    [​IMG]

    the answer is this:
    [​IMG]
    Though im not quite sure what b and c are.

    i guess for reference here is what it looks like after transforming it some:
    [​IMG]

    Here is the website if you need to do any clarification:
    http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/msp.html


    I have another problem similar to this for homework, i just wnat to see this one layed out before i work on my other. Thanks!
     
  2. jcsd
  3. [tex]

    mv_{x} + MV_{x} = C1

    [/tex]

    [tex]

    \int(-BV_{y})dt + \int(-KY)dt + MV_{y} + mv_{y} = C2

    [/tex]

    [tex]

    v_{x} = V_{x} + lsin(\varphi)\frac{d\varphi}{dt}

    [/tex]

    [tex]

    v_{y} = V_{y} + lcos(\varphi)\frac{d\varphi}{dt}

    [/tex]
     
  4. um, could you clarify a little bit more?
    my main problem is understanding the relationship between the pendulum and the first mass, M
     
  5. uppercase symbols for M, small symbols for m.
    B is damping coefficient of damper attached on M and K is spring coefficient.
    apply momentum conservation on both x and y direction can get above equatiions.
    C1 and C2 are initial conditions.
    derivation of second equation will be force-acceleration equation.
    Not difficult to understant. just "Ft + MV + mv = a constant" in differential form.
    It's a second order system. If you re-arrange them, you can get simillar equations as that on the webpage you provided.
    If there's something missing, might be geometry equations.

    Good Luck.
     
    Last edited: Aug 26, 2009
  6. thanks i appreciate it. I just started a vibrations course and this problem is similar to what i have in homework. i tried looking tah the lagrange equations to get an idea on an answer so i can go back and do the system again using newtonian equations, though as of last night it has started making me rather frustrated :/ and honestly its the pendulum thats messing me up.
     
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