Biorhythms were very popular in the 1960s. You can still ?nd many Web sites today that o?er to prepare personalized biorhythms, or that sell software to compute them. Biorhythms are based on the notion that three sinusoidal cycles in?uence our lives. The physical cycle has a period of 23 days, the emotional cycle has a period of 28 days, and the intellectual cycle has a period of 33 days. For any individual, the cycles are initialized at birth. Figure 1.12 is my biorhythm, which begins on August 17, 1939, plotted for an eight-week period centered around the date this is being written, October 19, 2003.
It shows that my intellectual power reached a peak yesterday, that my physical strength and emotional wellbeing will reach their peaks within 6 h of each other on the same day next week, and that all three cycles will be at their low point within a few days of each other early in November. The date and graphics functions in Matlab make the computation and dis- play of biorhythms particularly convenient. Dates are represented by their date number , which is the number of days since the zeroth day of a theoretical calendar year zero. The function datenum returns the date number for any given date and time. For example, datenum('Oct. 19, 2003') is 731873. The expression fix(now) returns the date number of the current date.
The following code segment is part of a program that plots a biorhythm for an eight-week period centered on the current date.
t0 = datenum(mybirthday);
t1 = fix(now);
t = (t1-28):1:(t1+28);
y = 100*[sin(2*pi*(t-t0)/23)
sin(2*pi*(t-t0)/28) sin(2*pi*(t-t0)/33)];
plot(t,y)
1. Complete this program, using your own birthday, and the line, datetick, title, datestr, and legend functions. Your program should produce some- thing like Figure 1.12.
2. All three cycles started at zero when you were born. How long does it take until all three simultaneously return to that initial condition? How old were you, or will you be, on that date? Plot your biorhythm near that date. You should ?nd the lcm function helpful.
3. Is it possible for all three cycles to reach their maximum or minimum at exactly the same time?