The pdf file with figure$($s$)$ in computer printout shall be emailed to the instructor by the due date. Hand written equations are ok but hand sketch figure$($s$)$ will not be accepted.

The uniform square panel of mass $=64$ is suspended from point $C$ by the two rigid bodies of negligible mass at A and $B.$ In gravitational field, if $BC$ of length b$=9$ at $B$ suddenly breaks,

$(1)$ Calculate the tension $T$ of $AC$ in $x-y$ components at the instant when the break occurs. $(10\%)$

$(2)$ Calculate the tension $T$ in $AC$ when it is vertical. $(10\%)$

$(3)$ Plot the tension in $AC$ when it swings $45($measured from the horizontal$)$ to $90(20\%)$

$(4)$ Plot the linear and angular acceleration of the mass center of the square panel in $3$ oscillation periods. $(20\%)$

$(5)$ Plot the trajectory of point A and the mass center of the panel in $3$ oscillation periods. $(40\%)$