two masses are connected via three springs to each other and to the wa

Question

Two masses are connected via three springs to each other and to the wall at left and right. The equations of motion are -k_{1} x_{1}-k\left(x_{1}-x_{2}\right)=m_{1} \ddot{x}_{1} -k_{2} x_{2}-k\left(x_{2}-x_{1}\right)=m_{2} \ddot{x}_{2} Your job is to calculate expressions giving the position of each mass as a function of time using the diagonalization method discussed in class. This classic problem can be solved in a number of different ways, but I will not give you credit unless you solve using the diagonalization method from the course. Suppose the force constants of the left and right springs are k1= k2 =2 and that of the center spring is k=1 let the masses be m1=m2=1 the two masses are given initial displacements at t =0 of x1 ==1 and x2=0 the initial velocity of each mass at t=0 is zero