Question 2 (20 marks) A system is modelled by the second-order linear ordinary differential equation (ODE) below: dx(t) dx(t) +6 dt + 8x(t) = 0 dt? a) What type of system is this? Overdamped or critically damped system? i. State the system and the characteristic equation ii. Get the values for the roots (s& ) of the characteristic equation [2 marks) [2 marks] b) State the complementary solution including the calculated values of s, & sz [1 mark) The system is now forced by a ramp function such that: dax(t) dx(t) dt? + 8x(t) = 2t dt Initial Conditions: x(0) = 0 () c) Determine the particular solution 17 marks) d) What is the total solution? [8 marks)