Investigation 13.1: Constructing an O-C Diagram

Your teacher will assign you a system to observe by timing. For example, you may be asked to time when the street light changes from red to green, or when the next commercial starts on a TV show. What you will end up with are a set of observed times, the times at which the "important event" (whatever you are assigned to observe) has occurred. You should have observed ten occurrences (ten cycles) of this system.

1. Make a table to list all your observations, leaving space for 4 columns. Enter your actual observations in column 2.

2. Number your observations, starting with zero (astronomers and mathematicians often like to start numbering things at zero rather than one). These are the cycle numbers n for your observations. The observations themselves are the observed values O . Enter the cycle numbers in column 1 of your table. If you have observed 10 cycles, and start numbering them from zero, then your cycle numbers n will range from 0 to 9.

3. Take the observed time of your very first observation as the estimated epoch

4. Compute the difference between the first two observed times by subtracting the second from the first. Take this as your estimated period P.

5. Using your epoch to and period P, calculate the computed time Cn for each cycle you have observed. Enter these values in column 3 of your table.

6. For each cycle n, subtract the computed time Cn from the observed time On, which will give you the O-C values. Enter these O-C values in column 4 of your table. Note: Because you took the first observation as your estimated epoch, the first O-C value will always be zero. Because you also took the time between the first two observations as your estimated period, the second O-C value will also always be zero.

7. Plot a graph with cycle number n on the x-axis and O-C value on the y-axis.

   What does the O-C diagram tell you? Is this system perfectly periodic? Is your estimated period correct?