BEHAVIOUR OF A VEHICLE'S SUSPENSION SYSTEM
...ll be many other values of w that will cause the displacement (x) to first equal zero after 2 seconds). CONCLUSION In conclusion it has been found that the zero displacements within the first 30 seconds occur at t equals 5.784645208 seconds, 16.2389874 seconds and 26.7277 seconds. It has also been found that when w equals 0.815996899 s-1, the displacement equals zero metres after two seconds. Overall the behaviour of the vehicle’s suspension is an oscillating motion and it is variable. The maximum vertical displacement of it continually decreases during the 60 seconds. APPENDICES Microsoft Excel was used to calculate all of the required information. APPENDIX A To produce the plot of x = 0.25exp-0.05t[cos(0.3t) + 1/6*sin(0.3t)], the first step was to prepare an excel worksheet containing a table of x versus t. I made x = 0.25*exp(-0.05*t)*(cos(0.3*t) + 1/6*sin(0.3*t)) and t = 0, 1, 2, ………, 59, 60. Instead of typing in every number and calculating each successive x value, I highlighted the first x or y value, clicked on the lower right corner of the cell and dragged the mouse down to the required number of cells (i.e. Excel will continue the sequence of values). See Figure 1. Evaluation of the Function x = 0.25*exp(-0.05*t)*(cos(0.3*t) + 1/6*sin(0.3*t)) t= x= 0 0.25 1 0.238898858 2 0.207986538 3 0.161848486 4 0.105963737 5 0.046141292 6 -0.012018693 7 -0.063594203 8 -0.104706759 9 -0.132760902 10 -0.1465488 Figure 1: Sample of x versus t table. To generate the graph of x versus t, I selected the information to be graphed, clicked on the Chart Wizard icon in the Standard Toolbar, chose the X-Y Scatter Graph and selected various features to complete the plot. APPENDIX B I used the Excel Goal Seek function to solve the times that the displacement of the vehicle’s suspension system equals zero (when 0 £ t £ 30 (seconds)). Firstly, I gave an approximation to the value of t when x equals zero by referring to Graph 1 (i.e. When x first equals zero, t » 6 seconds). I made x = 0.25*exp(-0.05*t)*(cos(0.3*t) + 1/6*sin(0.3*t)). See Figure 2. Solutions to x = 0.25*exp(-0.05*t)*(cos(0.3*t) + 1/6*sin(0.3*t)) in the first 30 seconds t= 6 x= 5.46E-05 Figure 2 I selected the Goal Seek function and set the ‘x’ cell to the value zero by changing the ‘t’ cell. I repeated this procedure for the next two roots of my equation that were in the range 0 £ t £ ...