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4. (a) A spring system is shown in Figure 4. Through considering how the extension of each spring relates to the tension in the springs, use the conditions of static equilibrium to develop a set of simultaneous linear equations in the five nodal displacements 61, 02, 03, 6 and 8s due to the nodal forces W1, W2, W3, W4 and W5. Rewrite the equations as a matrix equation. [10 marks] (b) Calculate the nodal displacements when: Ka = 2 N/mm, Ký = 2 N/mm, Ke = 4 N/mm, Kd = 2 N/mm, Ke = 4 N/mm, Ky = 8 N/mm Kg = 2 N/mm and W1 = 8N, W2 = 8N and W3 = 16N, W4 = 8N and Ws'= 8N. Show your working in full. You can use a computational tool (e.g. Matlab. Excel) to solve the matrix equation obtained in part (a). [5 marks] K Ko K | W2 w 8 82 Kd K ✓ W, WA T OA K } K, fo WS Figure 4 (c) Two complex numbers are 21 and zz: (1 + i) 31 = 2 + 2i 1 - 1 Showing your working in full, convert 21 and z, into polar form and find (21 x 23) [5 marks]