Consider the system shown below that has a Gartesiat Ory condinate system fixed at $O$ where the $x-$axis is horizontal and the $y$ axis is vertical, The rotational displacettent $O(t)$ of the bar is toritive in an anti$-$dockwise direction.

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For the above system determine the following indontation clearly chowing all steps and appropriate reasoning

$1\mathrm{.}1$ 'Defermine the differential equation of motion of the har as it osclllates about ier pivet if the $(20)$ mass of the bar la $7\mathrm{.}3$ kg

$1\mathrm{.}2$ Solve the differemtial equation of motion of the har as it oscllates about its pivat; $(15)$

$13$ Plot a graph of the solotion of the differensial equation inclusive of the rotational displacement $(15)$ and the rotational velacity of the motion of the bar as it oscillates about iss pivot for a time corresponding tw the natural angular frequency: