Consider a two$-$block system moving in the gravity field shown in Fig. $2.$

The two blocks have the same mass m and are connected via a rigid, massless rod of length l$.$

As a result of the gravitational acceleration g$,$ block $1$ moves horizontally and block $2$ can only

move vertically. There is no friction in this system. Moreover, block $1$ is connected to a wall

via a linear spring that has a spring constant k and a negligible free length. Therefore, the

elongation of the spring is the position x of block $1$ from the wall. For block $2,$ its horizontal

distance to the wall is l and its vertical position is y as shown in Fig. $2.$ Answer the following

questions.

a$)$ Write down constraint equation$($s$)$ of the system. Does the system have schleronomic constraints or rheonomic constraints.

$($b$)$ How are virtual displacement x and y related to virtual displacement $?$

$($c$)$ Use the principle of virtual work to derive the equilibrium equation of the system Figure $2$: A tweblock system with a fin$-$