![TableForm[Table[{t, N[x[t] - y[t]]}, {t, 0, T1 + T2, 0.2}], TableHeadings→ {None, {"t", "x[t]-y(t)"}}, TableAlignments→Center, TableDirections→Row]](../HTMLFiles/Physics, Oscillations_150.gif){kind=small}
CREDIBILITY OF THE RESULTS (2nd PROBLEM: SAME WIDTHS, DIFFERENT FREQUENCIES)
We have studied both the experimental x(t) and the analytical y(t) solutions of the oscillation synthesis.
We are forming the table of the difference x(t) - y(t), for t = 0 (0.2) T1+T2.
| t | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1. | 1.2 | 1.4 | 1.6 | 1.8 | 2. | 2.2 | 2.4 | 2.6 | 2.8 | 3. | 3.2 | 3.4 | 3.6 | 3.8 | 4. | 4.2 | 4.4 | 4.6 | 4.8 | 5. | 5.2 | 5.4 | 5.6 | 5.8 | 6. | 6.2 | 6.4 | 6.6 | 6.8 | 7. | 7.2 | 7.4 | 7.6 | 7.8 | 8. | 8.2 | 8.4 | 8.6 | 8.8 | 9. | 9.2 | 9.4 | 9.6 | 9.8 | 10. | 10.2 | 10.4 | 10.6 | 10.8 | 11. | 11.2 | 11.4 | 11.6 | 11.8 | 12. | 12.2 | 12.4 | 12.6 | 12.8 | 13. | 13.2 | 13.4 | 13.6 | 13.8 | 14. |
| x[t]-y(t) | 0. | -1.77636*10^^-15 | -1.77636*10^^-15 | 3.55271*10^^-15 | 0. | 0. | -7.10543*10^^-15 | 0. | 0. | 7.10543*10^^-15 | 7.10543*10^^-15 | 0. | 1.06581*10^^-14 | 0. | 7.10543*10^^-15 | -1.77636*10^^-15 | 2.4869*10^^-14 | 8.21565*10^^-15 | -8.88178*10^^-16 | 7.10543*10^^-15 | 1.06581*10^^-14 | 1.77636*10^^-14 | 7.10543*10^^-15 | 0. | 0. | 0. | 3.55271*10^^-15 | -7.10543*10^^-15 | -3.55271*10^^-15 | -3.55271*10^^-15 | 0. | -3.55271*10^^-14 | -3.55271*10^^-14 | -2.66454*10^^-15 | -9.99201*10^^-15 | -3.28626*10^^-14 | -1.77636*10^^-15 | -1.77636*10^^-14 | -8.88178*10^^-15 | -1.77636*10^^-15 | 0. | 0. | 0. | 1.06581*10^^-14 | 8.88178*10^^-15 | 1.77636*10^^-15 | 5.32907*10^^-15 | 1.77636*10^^-15 | 2.57572*10^^-14 | 2.04281*10^^-14 | 1.37668*10^^-14 | 0. | 2.77556*10^^-15 | 1.77636*10^^-15 | 3.10862*10^^-15 | 9.32587*10^^-15 | 8.88178*10^^-15 | -1.42109*10^^-14 | -1.59872*10^^-14 | -8.88178*10^^-15 | -1.18329*10^^-30 | -2.62013*10^^-14 | -1.46549*10^^-14 | -1.28786*10^^-14 | 4.44089*10^^-16 | -1.37668*10^^-14 | 1.06581*10^^-14 | -6.66134*10^^-15 | 1.66533*10^^-15 | 1.16573*10^^-14 | 3.55271*10^^-14 |
Questions:
1) Does the analytical solution of the composite oscillation differ from the experimental solution?
2) If there are differences between the analytical and the experimental solution of the composite oscillation, where do you think they can be attributed?
EXERCISE:
Using the commands and programs presented above, study the same problem for another set of values A1 = A2 and frequencies w1, w2.
Are the results on the former two questions similar?
| Created by Mathematica (November 4, 2015) |  |