For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system is originally at rest. Briefly interpret physical significance of the modal shapes. respect the mass and stiffness matrices, respectively. i.e. 4. What are the generalized mass and stiffness coefficients for each mode? 5. Is the system damping is a classical one and why? 6. What are the system kinetic energy and elastic potential energy in terms of x1 and x2 and their first-order derivatives? For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system is originally at rest. Briefly interpret physical significance of the modal shapes. respect the mass and stiffness matrices, respectively. i.e. 4. What are the generalized mass and stiffness coefficients for each mode? 5. Is the system damping is a classical one and why? 6. What are the system kinetic energy and elastic potential energy in terms of x1 and x2 and their first-order derivatives?