Consider the two-mass, three-spring system whose equatio

Consider the two-mass, three-spring system whose equations of motion are Eqs. (11) in the text. Let m1 = m2 =1 and k1 = k2 = k3 = 1. (a) Using the values of the parameters given in the previous statement, find the eigenvalues and eigenvectors of the matrix A. (b) Write down the general solution of the system. (c) For each fundamental mode, draw graphs of x1 versus t and x2 versus t and describe the fundamental modes of vibration. (d) Consider the initial conditions x(0) = (?1, 3, 0, 0)T . Evaluate the arbitrary constants in the general solution in part (b) and plot graphs of x1 versus t and x2 versus t. (e) Consider other initial conditions of your own choice, and plot graphs of x1 versus t and x2 versus t in each case.