Thursday, February 7, 2008

1.10: Periodic Functions.

Main Points
Periodic functions have graphs that look like waves as their values repeat after fixed time periods and this goes on forever. The sine and cosine graphs are the most common periodic functions there are and the graph of the cosine function is the same as that of the sine graph only shifted "pi"/2 to the left. Both have an amplitude of 1 and a period of 2*"pi". Periodic functions come with a family with the general term: y = A sin(Bt) where A and B are parameters. "A" affects the amplitude of the graph and "B" affects the period. (the smaller B is the bigger the period.)

Challenges
Are the functions called periodic simply because they have a constant period? Does that mean that if the period were constant but the amplitude of the graph changed it would still be a perfectly good periodic function? Period is equivalent to wavelength right? Therefore light can be considered periodic until it moves from one medium to another and the wavelength changes...
Is this right?

Reflections
Considering that periodic functions are supposed to repeat basically forever applying the functions to real life situations allows the user to predict and therefore prepare for the future. Granted the data would not fit perfectly on a sin curve but it would suggest such as for the housing project that the builders would be able to project would rough amounts of concrete they would be needing.

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