Problem $3$: Consider the following inverted pendulum that consists of a massless bar of length $L=0\mathrm{.}5$ m and a point mass $m=1kg$ located at the tip of the bar. The inverted pendulum is free to rotate about the fixed pivot point $0.$

i$)$ Find the equation of motion of the bar with respect to the rotating angle $.$

ii$)$ Find the linearized equation of motion about the vertical position $\frac{?}{\text{b}\text{a}\text{r}}()=0$