The displacement, x, of an oscillating spring in a vehicle accelerating uniformly with respect to a...

 

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The displacement, x, of an oscillating spring in a vehicle accelerating uniformly with respect to a point on the ground is modelled using the function x = 0.5 +0.25t + 2t² where t is time. It is shown in Figure 5 below 45 40 35 30 25 20 15 10 5 0 0 0.5 1 - 2cos (10t) 1.5 2 1 2.5 3 Figure 5 Displacement of an oscillating spring in a vehicle. 3.5 4 a. Differentiate the function with respect to t. (6 marks) b. Apply the Newton-Raphson method to (t) to find all three points where x(t) is zero to an accuracy better than 0.0001. Give your answer to 4 decimal places. (16 marks) Hint: your starting 'guess' 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. The displacement, x, of an oscillating spring in a vehicle accelerating uniformly with respect to a point on the ground is modelled using the function x = 0.5 +0.25t + 2t² where t is time. It is shown in Figure 5 below 45 40 35 30 25 20 15 10 5 0 0 0.5 1 - 2cos (10t) 1.5 2 1 2.5 3 Figure 5 Displacement of an oscillating spring in a vehicle. 3.5 4 a. Differentiate the function with respect to t. (6 marks) b. Apply the Newton-Raphson method to (t) to find all three points where x(t) is zero to an accuracy better than 0.0001. Give your answer to 4 decimal places. (16 marks) Hint: your starting 'guess' 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.