3. For the following undamped 2-DOF system with data and the equations of motion: (a) determine the two natural frequencies of the system, (b) determine the two normal modes (eigenvectors) of the system, (c) write-out the normal modal matrix [P], (d) diagonalize the stiffness matrix using the normal modal matrix [P], (e) diagonalize the mass matrix using the normal modal matrix [P], (f) determine the orthonormal modal matrix [P]. (g) What is the solution vector given the following data and initial conditions. Data: mi = 10 kg, m2 = 1 kg, k₁ = 30 N/m, k2 = 5 N/m, k3 = 0, and x1 (0)= x2 (0)=x2 (0)=0, x1(0)=1m mi 0x1 -k2 Sor + = 0 m2 2 -k2 k₂+k3x2)