### The following system of equations represents the motion of two blocks connected by springs. The positions of the blocks are given by the functions ( x_{1}(t) ) and ( x_{2}(t) ) [ begin{array}{c} ddot{x}_{1}+4 x_{1}=4 x_{2}+5 \ ddot{x}_{2}+3 x_{2}=2 x_{1}+2 end{array} ] (a) Express the system as a matrix equation. (b) Using matrix methods, find the

The following system of equations represents the motion of two blocks connected by springs. The positions of the blocks are given by the functions ( x_{1}(t) ) and ( x_{2}(t) ) [ begin{array}{c} ddot{x}_{1}+4 x_{1}=4 x_{2}+5 \ ddot{x}_{2}+3 x_{2}=2 x_{1}+2 end{array} ] (a) Express the system as a matrix equation. (b) Using matrix methods, find the