QUESTION 2 Seismic friction dampers can be used to damp the oscillations of a building during an earthquake and can be modelled by the following system of first order linear equations: x' = Ax = (2)-(6-3)() X2 a) Find the general solution of the system by performing the following steps: i) Determine the characteristic polynomial. [2 marks] ii) Determine the eigenvalues of the system. [2 marks] iii) Determine a corresponding eigenvector for each eigenvalue. [6 marks] iv) Write out the general solution of the system. b) At time t=0s, the system has the following initial conditions: xo = x(t = 0) = (2) Determine the particular solution of this system. [2 marks] [3 marks] c) Sketch the phase plane for this system. Determine the type of critical point at the origin and state whether the behaviour of the system is stable or unstable. [Total marks: 20] [5 marks] Semester 2 2023-2024 KL5002: Further Mathematics Page 3 of 8