- The initial displacement angle must be set for each replicate measurement of the period " T ", and this angle is assumed to be constant.
- Since " ? " is the single time-dependent coordinate of this system, it might be better to use " ? 0 " to denote the initial ( starting ) displacement angle, but it will be more convenient for notation to omit the subscript.
- The procedure is to measure the pendulum length " L " and then make repeated measurements of the period " T, " each time starting the pendulum motion from the same initial displacement angle " ? . " The replicated measurements of " T " are averaged and then used in Eq ( 2 ) to obtain an estimate of " g ".
- where the ? " L " etc . represent the biases in the respective measured quantities . ( The carat over " g " means the estimated value of " g " . ) To make this more concrete, consider an idealized pendulum of length 0.5 meters, with an initial displacement angle of 30 degrees; from Eq ( 1 ) the period will then be 1.443 seconds.