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Modelling: Second Order System

  1. May 10, 2015 #1
    I have attached an image of a question I am trying to do, I want to find the differential equations that describe the second order system in the image.

    I know for a spring, potential energy = 1/2.K.x (where k is the spring constant, and x is the distance the spring is stretched).

    I know that damper dissipation is = 1/2.B.(dx/dt) (where B is the damping constant and dx/dt is the rate of change of position with respect to time).

    My solution:

    I try to build a free body diagram for each mass on its own:

    I have showed a snapshot of my attempt for the D.E. describing the motion of m1.

    If any of you guys could tell me if I am correct or you have a handy way of doing these types of questions please feel free to respond.

    Thank you
     

    Attached Files:

  2. jcsd
  3. May 10, 2015 #2

    BvU

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    Hello Mark, welcome to PF :smile: !

    For some reason the template has disappeared. Pity (*). The relevant equation is ##\Sigma F = ma##. So you want to sort out the signs a little more carefully (of the forces; ##-k## is not a force, nor is ##-B## ).


    (*) Its use is mandatory in PF, for very good reasons; see the guidelines.
     
  4. May 10, 2015 #3
    Hi BvU,

    Apologies about the template, I will not post without a template again.

    My notation there was a little careless, I did not mean to label K and B as forces, I was trying to imply that there is a force acting on mass m1 due to both the spring and the damper.

    Spring: k.x1
    Damper: B.(x2dot-x1dot)

    And that these two forces oppose the motion of mass m1 from left to right.
     
  5. May 10, 2015 #4

    BvU

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    is good. And when you state that, you should also write something like ##m_1\ddot x_1 = -kx_1## and not e.g. ##m_1\ddot x_1 -kx_1 = 0 ## :rolleyes:
     
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