Consider weights W$1,$ W$2$ and W$3$ supported by the linear springs shown in the figure below. The spring constants are k$1,$ k$2$ and k$3.$ Determine the displacements q$1,$ q $2$ and q$3$ of the weights as functions of W$1,$ W$2,$ W$3,$ k$1,$ k$2$ and k$3($using energy method$).$ Assume that the weights are applied slowly so that the system is always in equilibrium as the springs are stretched from their initially unstretched lengths $(10$ marks$).$