Axial eccentric loading on self-weight deflected cantileaver

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Waleed Shaukat
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Homework Statement


Hello,

I am trying to model an arm mounted perpendicular to the straight mechanical column. An arm can be translated in horizontal direction by a gear which engages with the bottom of an arm such that it applies no force in vertical direction to the arm. And finally there is a gauge attached to the free working end of the arm.

For ease, I have taken this gauge weight to be a point load acting at the end of the arm. And the arm has been assumed to be a mass-less cantileaver beam of rectangular section on to which its weight has been assumed to be an external equally distributed load.

I am now required to derive the model of this beam (arm) with small deflection already induced by its weight (has been derived) been subjected to the axial force by the turning of the gear that results in the deflected beam getting dynamic( that is oscillating from the end) and increased in size as the free length of the arm is increased horizontally.

Homework Equations

The Attempt at a Solution

 
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How to develop as accurate physics-based dynamic model as possible?
 
A picture sure would help.