A system is modelled by the second-order linear ordinary differential equation (ODE) below: d2x(t) +6 dx(t) + 8x(t) = 0 dt dt a) What type of system is this? Overdamped or critically damped system? i. State the system and the characteristic equation [2 marks] ii. Get the values for the roots (s, & sz) of the characteristic equation [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: d2x(t) + 6 dt2 dx(t) dt + 8x(t) = 2t Initial Conditions: x(0) = 0 dx dt = 0 tad = c) Determine the particular solution [7 marks] d) What is the total solution? [8 marks]