Q$4$: A $26$ meter uniform rectangular plate of mass $100$ kg dilu centroidal mass moment of inertia $333kg-m2$ is connected to a pin at A and a spring at $B.$ The spring has an unstretched length of $4$ meters and a spring constant of $k=100\frac{N}{m}.$ The plate is held and released from rest in the position shown in the sketch $($also select horizontal line $AB$ as the Datum$).$ The plate will swing down with gravity to be rotated through $90$ degrees

$(1)$ Is this system Conservative? $($Circle one$)$

Yes No

$(3)$ Write the Energy Balance Equation$($s$).$

Find the value of the angular velocity of the plate after it has rotated through $90$ degrees.