The displacement, :13, of an oscillating spring in a vehicle accelerating uniformly with respect to a point on the ground is modelled using the function a: (t) = 0.5 + 0.25: + 2:2 2cos (10:) where t is time. It is shown in Figure 5 below 45 40 35 30 _5 I 1 I I 0 0.5 | [.5 2 2.5 3 3.5 4 I Figure 5 Displacement of an oscillating spring in a vehicle. Figure 5 Displacement of an oscillating spring in a vehicle. a. Differentiate the function with respect to t. (6 marks) b. Apply the Newton-Raphson method to t) to nd all three points where t) is zero to an accuracy better than 0.0001. Give your answer to 4 decimal places. (16 marks) Hint: your starting iguess' will determine to which solution the method converges. Try t= 0.5 first. Then try other starting values close to the solution to which you wish to converge. Show your workings in a table