Problem $3-$ Linear graph of system with one$-$port elements

A$1.$ Draw a linear graph for the mechanical system shown below.

A$2.$ Derive the state$-$space representation selecting as states the velocities of the two

masses and the force of the spring, and using the spring force as the output.

B$1.$ Consider the same system subject to a velocity source $($velocity of mass $2$ regulated

by a source$).$ Draw the graph of this second system.

B$2.$ Derive the state$-$space representation for the system subject to a velocity source.

Please discuss if the system has now two or three states.

B$3.$ For the system subject to a velocity source, what is the force that the velocity source

needs to apply as a function of $v_2^{},v_2,$ and $v_1?$