A uniform horizontal sign post has a mass M and length L, and is fixed at one end to a vertical pole. A support cable, which makes an angle theta with the horizontal, stabilizes the sign post. A bird of mass $m$ lands on the post, positioned a distance $x$ from the pole. Determine the vertical and horizontal components of the force exerted by the sign post on its fixed point (pole) as a function of $x$ .

$F_{\(\text{vert }\)}=mg\(\left\)(\(\frac{x}{L}\]\right\))+Mg;\ F_{\(\text{horiz }\)}=\(\frac{mg}{L\sin \theta }\)x+\(\frac{Mg}{\tan \theta }\)$

$F_{\(\text{vert }\)}=mg\(\left\)(1-\(\frac{x}{L}\]\right\))+\(\frac{1}{2}\)Mg;\ F_{\(\text{horiz }\)}=\(\frac{mg}{L\tan \theta }\)x+\(\frac{Mg}{2\tan \theta }\)$

$F_{\(\text{vert }\)}=mg\(\left\)(\(\frac{x}{L}\]\right\))+\(\frac{1}{2}\)Mg;\ F_{\(\text{horiz }\)}=\(\frac{mg}{L\tan \theta }\)x+\(\frac{Mg}{\tan \theta }\)$

$F_{\(\text{vert }\)}=mg\(\left\)(2-\(\frac{x}{L}\]\right\))+\(\frac{1}{2}\)Mg;\ F_{\(\text{horiz }\)}=\(\frac{mg}{L\cos \theta }\)x+\(\frac{Mg}{2\cos \theta }\)$