Use state space analysis in Matlab to construct a numerical solution to the two$-$mass three$-$spring assuming the masses each have mass $1$ kg and each spring has constant $k=1\frac{N}{m}$ for the initial conditions: i$)x_1(0)=1$;$x_2(0)=1$;$x_1^{}(0)=x_2^{}(0)=0,$ ii$)x_1(0)=1$;$x_2(0)=-1$;$x_1^{}(0)=x_2^{}(0)=0,$ iii$)x_1(0)=0\mathrm{.}5$;$x_2(0)=-1$;$x_1^{}(0)=x_2^{}(0)=0.$ Plot the solutions from tin$[0,10].$ Use the output functionality to describe the solution in terms of the center of mass and relative coordinates from an earlier homework. Describe your solutions in terms of the normal modes of the system.