Problem $4(25$ points$)$:

In Figure $4,$ a $5-$kg uniform serving table is supported on each side by two pairs of identical links, $AB$ and $CD,$ and springs $CE.$ If the bowl has a mass of $1kg$ and is in equilibrium when $=45,$ and the springs of stiffness $k$ each are unstretched when $=90.$ Neglect the mass of the links.

$($a$)$ Draw the free body diagram. You need to specify the positions of the gravity center of the bowl $(y_{Gb})$ and table $(y_{Gt})$ as well as the deformation of the spring $(x_C)(5\%)$

$($b$)$ Express $y_{Gb},y_{Gt}$ and $x_C$ in terms of $.(5\%)$

$($c$)$ Find the virtual displacements $y_{Gb},y_{Gt}$ and $x_C$ of the positions due to a virtual rotation $.(5\%)$

$($d$)$ Write the virtual work equation. $(5\%)$

$($e$)$ Determine the stiffness of each spring. $(5\%)$

Figure $4$