$(5$ Points$)$ The bar with length $L$ and mass $m$ slides through the double collar $C$ with no friction. The springs at C and A have stiffnesses $k_C$ and $k_A.$ The angle $$ is a constant $60$ degrees. When $=30$ degrees and $x=0\mathrm{.}6m,$ both springs are unstretched. Find the EOM for the bar, working in the I frame with the two DOF being $x$ and $$ and defined as positive displacements shown in the picture. Suggestions: Define the stretch of the length of the spring at C as $L_2$ and the length from A to C as $L_1$ and leave them as a function of x and $$ in your EOM. Also look at lesson $16$ and set up the solution as $33$ matrix with the two state accelerations ${}^{}$ and $x^{}$ and the normal force at A $($This will save a lot of algebra.$)$