1) Choose a famous city ((London)
2) From weather.com get a 24h, hour by hour forcast for any given day. Print it out for your record as you will need to include this in your report.
(Please attache it to me in this order)
3) Plot the hour by hour temperatures and find the best values of a, b, w, and d such that M(t)= b + a sin(w t + d) fits best your data. This will require playing around with different values of a, b, w, and d until you are happy with the fit. It will be a good idea to plot both M(t) and the hour by hour temperatures to see how good the fit is.
4) Solve Newton’s cooling law with the M(t) found in (3)
5) Plot many solutions with different initial values T(0) and using different values of k. Comment and interpret your results, and pick the value of k that seems to be the most reasonable one. Of course proper justification needs to be given.
6) You are to set up a nursery for premature babies in your city. The temperature inside this building should strictly be between 24 and 27 degrees. Is it possible to achieve this goal without heating and air conditioning?
7) If the answer to 6) is yes contact me immediately. If the answer is no, then add +h or -h to the right hand side of Newton’s cooling law. Choose the right value of h and see how close you get to achieve your goal (if at all possible). This again needs some experimentation with different values of h.
8) Using air conditionning and heating is actually costly. Improving the value of k of the building is also costly. How do we find a trade off?
9) Write a report 1-3 pages on the above. Put graphs, experimentations and lengthy calculations in the appendix. This project has a lot of experimentation in it and should be reflected and detailed in yoiur report and in your appendix.