Page 354 - MATLAB an introduction with applications

Direct Numerical Integration Methods ——— 339

The output of the program is shown below for various values of ∆t.
when ∆t =1 sec, the following results are obtained
time displacement velocity acceleration
0.000000 0.000000 0.000000 1.000000
1.000000 0.500000 0.590965 0.181930
2.000000 1.181930 0.433220 –0.497419
3.000000 1.366441 –0.144974 –0.658969
4.000000 0.891982 –0.606607 –0.264297
5.000000 0.153226 –0.536092 0.405328
When ∆t = 0.5 sec, the following results are obtained
time displacement velocity acceleration
0.000000 0.000000 0.000000 1.000000
0.500000 0.125000 0.407252 0.629008
1.000000 0.407252 0.620473 0.223877
1.500000 0.745473 0.638891 –0.150209
2.000000 1.046143 0.491762 –0.438307
2.500000 1.237235 0.231599 –0.602342
3.000000 1.277742 –0.075255 –0.625078
3.500000 1.161980 –0.359295 –0.511081
4.000000 0.918447 –0.558261 –0.284782
4.500000 0.603719 –0.625966 0.013962
5.000000 0.292481 –0.538461 0.336057
When ∆t = 0.1 sec, the following results are obtained
time displacement velocity acceleration
0.000000 0.000000 0.000000 1.000000
0.100000 0.005000 0.096651 0.933023
0.200000 0.019330 0.186429 0.862537
0.300000 0.042286 0.269009 0.789068
0.400000 0.073132 0.344120 0.713147
0.500000 0.111110 0.411543 0.635310
0.600000 0.155441 0.471113 0.556092
0.700000 0.205332 0.522719 0.476028
0.800000 0.259985 0.566303 0.395644
0.900000 0.318593 0.601858 0.315459
1.000000 0.380356 0.629430 0.235982
1.100000 0.444479 0.649114 0.157706
1.200000 0.510179 0.661055 0.081110
1.300000 0.576690 0.665443 0.006652
1.400000 0.643268 0.662514 –0.065229
1.500000 0.709193 0.652547 –0.134117
1.600000 0.773777 0.635860 –0.199624
1.700000 0.836365 0.612810 –0.261384
1.800000 0.896339 0.583787 –0.319064
1.900000 0.953122 0.549216 –0.372359