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Homework Help: Equation of Motion for 2 DOF spring damper system

  1. Apr 14, 2009 #1
    Please guide me towards the "differential equation of motion" for the following 2 DOF Spring-damper system.


    And furthermore, if above system is in a uniform speed rotating frame, then what can be the effect on this system?

    Thank you very much.
  2. jcsd
  3. Apr 15, 2009 #2


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    Please write the equation for one dof.

    Does gravity g apply to y-direction?

    What force must be considered in a rotating body?
  4. Apr 15, 2009 #3
    Thank you for your reply.

    m*(d2x/dt2)+c*(dx/dt)+k*x = 0 is the equation for one axis.

    No effect of gravity is considered here.

    The whole frame is rotating at an uniform angular velocity.

    If you can provide equation for static (i-e. not rotating) case, that's also fine.
  5. Jun 2, 2011 #4
    Correct me if I'm wrong.

    Here are the motion equations;

    mx'' + c1x' + k1x' = 0 (Not forced)
    my'' + c2y' + k2y' = 0 (Not forced)

    Suppose the frame is rotated thru angle q,

    In this case, the mass center position with respect to the frame F is

    Xnew = x*cos(q) - y*sin(q)
    Ynew = y*cos(q) + x*sin(q)

    You can simply differentiate Xnew and Ynew. Once and twice, then replace in motion equations

    Xnew' = cos(q)*(x'-yq*') - sin(q)*(y'+xq*')
    Xnew'' = x''*cos(q) - 2*x'*q'*sin(q) - x*q''*sin(q) - x*q'*q'*cos(q)
    -y''*sin(q) - 2*y'*q'*cos(q) - y*q''*cos(q) + y*q'*q'*sin(q)

    Note that q''=0. Eliminate some of the terms above and do the same thing for y-axis
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