Engineering Simulations and Computations - ENG3104 - Engineering Assignment Help

Assignment Task

Introduction
This question is concerned with the motion of Particle 1 in Assignment 1. Several numerical schemes are to be employed to compute the velocities and accelerations of the particle.
From the first three columns of the data table in file <A1_input.txt> (i.e. values of t, x and y for Particle 1), you will need to generate three sets of data: Set A, Set B and Set C that comprise, respectively, the following rows
1, 11, 21, · · · , p, q, · · · , · · · , N (q = p + 10),
1, 6, 11, · · · , p, q, · · · , · · · , N (q = p + 5),
1, 2, 3, · · · , p, q, · · · , · · · , N (q = p + 1),
where N is the number of time points in the data file (N = 101). Figure 1 displays the three data sets on x-y plane. It can be seen that (i) the first and second time points are 0 and 0.6626 s in Set A, 0 and 0.3345 s in Set B, and 0 and 0.0675 s in Set C, and (ii) Set C is identical to the data set for Particle 1 in the file. Your first task is to employ three numerical schemes, namely forward, backward and central difference schemes for first derivative, to compute the velocities and accelerations of the particle for Set C. Your second task is to study the influence of time step (grid size) on the approximation quality of the backward difference scheme by considering the three data sets. Let vx and vy be the x and y components of the velocity vector, and ax and ay be the x and y components of the acceleration vector.

Requirements
For this assessment item, Set C is considered and you must perform hand calculations:
1. Employ the three numerical schemes to estimate vx and vy of the particle at tk, where k is obtained by using Matlab function <round> to round the following value to the nearest integer [5 + 6.9479] (this value is not to be shared with anyone else). For example, if k = 11, one has tk = 0.6626 s. Report the answers in engineering conventional form.
You must also produce MATLAB code which:
2. Loads the data file <A1_input.txt> into Matlab and from the first three columns (the data set for Particle 1 in the file), repeat the hand calculations. Verify the answers by
using the reported results from Requirement 1.
3. Employs the three numerical schemes to compute vx, vy, ax and ay of the particle at all time points for Set C, where loops are used (scalar-based calculations). Verify the results vx and vy obtained at tk with those from Requirement 2.

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