Laboratory Help Page

This page is designed to provide helpful information about the laboratory questions.

Because of the upcoming Exam, you will have two weeks to work this laboratory. Begin this lab and every lab by introducing yourself to your partner. Find times when you can meet together during the week before the lab is due on Friday, Oct. 13. If your schedules are totally incompatible, then notify me immediately.

You will probably want to download your specific lab page (and may want to convert it to a Word document). On the cover page you begin by typing in the name of each team member and your group number.

Question 1: This problem gives you practice determining the period of a periodic function. The y-value of the maximum and minimum should be easy to obtain by simply using the fact that the cosine function has a maximum value of 1 and a minimum value of -1. The x-values at the extrema are most easily found using Maple's fsolve function, but many can also be found by interpreting the periodicity of the function. This is primarily a graphing exercise, which uses those capabilities of either Excel or Maple. Below shows you one means of entering the sum of two functions into Maple:

Enter the two functions, f(x) and g(x) as before

> f := t -> cos(3*t); g := t -> cos(5*t);

Combine the functions

> F := t -> f(t)+g(t); F(t);

Putting in the additional F(t) makes Maple print out the correct function for you. Notice that, because Maple is case sensitive, we can use f(t) and F(t) as different functions.

Question 2: This problem asks you to go to a data base, then calculate the length of the day in minutes. Based on the table from the Navy, you find the appropriate scaling factors to substitute in for the parameters in the basic trigonometric function. The directions in the problem should provide you with the tools that you need. You may find it interesting to see that the earliest and latest sunsets and sunrises do not occur on the shortest and longest days of the year due to the elliptical nature of Earth's orbit.

Question 3: The last question is another optimization problem. In this problem, you want to carefully go through each step of the problem, finding the quantities requested. You can differentiate the energy function by Maple, but it is probably a good idea that you do it by hand for additional practice. Again the steps are laid out in order in the lab, so little additional help should be necessary.