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Lagrange EOM for 2 masses on a string

  1. Mar 16, 2015 #1
    1. The problem statement, all variables and given/known data

    Derive the equation of motion for the system in figure 6.4 using Lagrange's equations


    upload_2015-3-16_18-26-58.png

    2. Relevant equations
    m1=.5m
    m2=m
    strings are massless and in constant tension

    Lagrange=T-V

    3. The attempt at a solution
    I currently have the kinetic energy as .5m1y'12 + .5m2y'22

    I am confused regarding the potential energy of the system. I understand each mass will have an m*g*y component associated with them but i am unsure how the tension plays into the potential energy. Once i have the potential energy for the system i can take it from there. Any advice would be greatly appreciated, thanks!
     

    Attached Files:

  2. jcsd
  3. Mar 16, 2015 #2
    Greetings,
    So here is the how to 1:Short document:
    Find me EoM!
    2:Long video:

    Note: I am going to get some sleep....If that is not what you asked for, please wait for someone else to answer you or @ToBePhysics so I can get to you when I am done doing things.
     
    Last edited: Mar 16, 2015
  4. Mar 16, 2015 #3
    Hmm interesting video but I am afraid something is just not clicking for me with regards to this problem.

    for the potential energy there will be a m1gy1 term and a m2gy2 term. I assume there must also be terms for the work done by the tension in the strings, but only the y components as these are only given one DOF each. That would give a Ty1sin(θ1) and Ty2sin(θ3) correct? assuming θ1 is the angle between the left wall and that string and θ3 is the angle between the right wall and the attached string.

    My confusion is coming when i need to take into account the string attaching the two masses. Is my logic correct thus far?
     
  5. Mar 17, 2015 #4
    W=P.Ef-P.Ei=K.Ef-K.Ei.
    I don't know much about strings...But I am trying my best gathering resources that help..
    Sometimes:
    E.P.E=K.E
     
  6. Mar 17, 2015 #5
    Hmm not sure that helps me a ton unfortunately.. i am reallly struggling to wrap my head around this potential energy problem.
     
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