b) Given that xo = 0.0, x; = 0.8 and a = 0.2 determine the positions x2 to xs of the mass by solving the matrix equation in part a) of this question and assuming that 0 0 0 0 0 0 1 0 0 Q-2) 1 0 0 1.80 1 0 (2-2) 1 0 2.24 Rue 1 0 1 (Q-2) 1 2889 2.24 1.80 1 2.232 C) Assume m=1kg and k=1 N/m, hence deduct At. [10 marks] Comment on the realism of the results of part b). TE media 2. This question relates to the motion of a spring on a mass, such as found in the suspensi system in a car and involves the solution of a second order differential equation using mat methods. a) The equation of motion of a mass spring system is given by the following equation: m dt = -kx (2.1) Briefly explain the meaning of each term and using the following relationship (2.2) dx dt? Xn+1-2Xn+Xn-1 t 2 (2.2) transform the equation (2.1) above into a simple matrix equation for 4 consecutive positions of the mass, assuming x, and xy are known and that a = kat2 Show that: m 062 1 (a -2) 1 0 0 1 (a-2) 1 0 0 0 0 1 0 (a-2) 1/ --xo - (a - 2)x; -X1 X4 X5 [10 marks b) Given that xo = 0.0, x1 = 0.8 and a = 0.2 determine the positions xy to xs of the mass b solving the matrix equation in part a) of this question and assuming that (2-2) 1 0 0 1 (a-2) 1 0 0 0 0 1 0 (a-2) 1/ 1 0 0 1.80 1 0 2.24 1.00 1 2.832 2.24 1.80 0 0 0 1 [10 marks c) Assume m=1kg and k=1 N/m, hence deduct At. Comment on the realism of the results of part b)