$(30$ Points$)$ The particle is held between the forked rod and the curved track. The particle has a mass of $m=0\mathrm{.}1kg.$

The equation for the track is $r=A{e}^{},$ where $A=2m.$ The rod starts at rest at $=0$ rad and accelerates counter$-$

clockwise with ${}^{}=0\mathrm{.}5ra\frac{d}{s^2}.$ Calculate the magnitudes of the forces acting on the particle at $t=3s.$ Draw your force

vectors in the appropriate directions. Gravity acts into the page.