the system shown below that has a Cartesian Oxy coordinate system fixed at O where the z$-$axis is horizontal and the y$-$axis is vertical. The rotational displacement $0($t$)$ of the bar is positive in an anti$-$clockwise direction.$-5$ m$2$ rad$/$sk $=6$ N$/$m$4$ m$3$ mFor the above system determine the following information clearly showing all steps and appropriate reasoning:$1\mathrm{.}11\mathrm{.}21\mathrm{.}3$Determine the differential equation of motion of the bar as it oscillates about its pivot if the mass of the bar is $7\mathrm{.}3$ kg;Solve the differential equation of motion of the bar as it oscillates about its pivot;Plot a graph of the solution of the differential equation inclusive of the rotational displacement and the rotational velocity of the motion of the bar as it oscillates about its pivot for a time corresponding to the natural angular frequency;$(20)(15)(15)$