# Equations of motion for a motor supported by a spring resting at the centre of a beam 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 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 -.

• What are kx and ktheta? I don't see them in the diagram. It is not clear what you are asking. Jan 13 '19 at 18:01
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– Wasabi
Jan 13 '19 at 19:06
• They are using small angles approximation, and since the beam rotates one of the point goes up and other down. Jan 14 '19 at 21:19
• 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.
– SF.
Jan 15 '19 at 9:21