Problem 1: File-A, Problem 3.1(see remarks on models) [1] by longhand calculation [2] by Matlab function eig use the following data: k=200 N/m, m=2 kg. [3] show the components of rations of eigenvectors computed by longhand solution and by eig is a constant vector. Remarks on models The models shown in Figure3 P3,3 P.3.7 (with dampers) are equilavent to the 2-dof spring-mass model of Problem T-1. Figure P2.6 is a 3-dof spring-mass model. Problems 3.1 For the 2-DOF system shown in Figure P.3.1, let k =k, k, m,m,m. Find the natural frequencies and the associated mode shapes of the system. Ans: 2 k2 1 m Figure P3.3 =0.618, F {0}={1 1.618 1.618 m {0}={1 -0.618}'