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Equation of Motion of Mass Damper and Rotating Bar

  1. Sep 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Consider the inverted pendulum system, where a uniform rigid bar of mass m and length L is elastically hinged on top of a lumped mass M. The bar is constrained by a torsional spring of coefficient kτ and the mass is constrained by a damper of coefficient c. Derive the nonlinear equations of motion for the system by the Newtonian Method.


    3. The attempt at a solution
    I have drawn the FBD of each mass and got the separate equations of motion:

    For mass M:
    M[itex]\ddot{x}[/itex]+c[itex]\dot{x}[/itex] = F(t)

    For rotating bar:
    J[itex]\ddot{θ}[/itex]+k[itex]_{τ}[/itex][itex]\dot{θ}[/itex] = 0

    where J = (1/3)mL[itex]^{2}[/itex], resulting in

    (1/3)mL[itex]^{2}[/itex][itex]\ddot{θ}[/itex]+k[itex]_{τ}[/itex][itex]\dot{θ}[/itex] = 0

    I am not sure how to relate the 2 in order to derive the nonlinear EOM. Any hints or suggestions would be greatly appreciated!
     

    Attached Files:

  2. jcsd
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