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Exam Question on Equations of Motion and Free Body Diagrams Assumptions from this:

  • Sum of forces on the beam to be calculated
  • Sum of moments on the beam to be calculated
  • Sum of forces on the motor to be calculated

As:

F=-kx = kθL^2

Equations of Motion

Beam

enter image description here

Question:

Would anyone be able to explain why the + and - L/2theta are the way they are?

I believe I understand why k1 is positive and k2 are negative as taking moments about the centre, assuming clockwise is +ve, means that k2 opposes and k1 follows rotation but I don't understand how to assign L/2 a + or -.

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  • $\begingroup$ What are kx and ktheta? I don't see them in the diagram. It is not clear what you are asking. $\endgroup$
    – Daniel K
    Jan 13 '19 at 18:01
  • $\begingroup$ Welcome to Engineering! This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. $\endgroup$
    – Wasabi
    Jan 13 '19 at 19:06
  • $\begingroup$ They are using small angles approximation, and since the beam rotates one of the point goes up and other down. $\endgroup$
    – joojaa
    Jan 14 '19 at 21:19
  • $\begingroup$ Seems like one is + and the other is - because they are the components responsible for the beam rotating, so if it turns, one end goes down, the other end goes up. Other components are responsible for translational movement. The choice of which one is '+' and which one is '-' is arbitrary, depending on which turn direction corresponds to theta growing. $\endgroup$
    – SF.
    Jan 15 '19 at 9:21

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