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interrupt time data from a photogate by a clock pendulum is very noisy. In order to analyze and display (graph), it's necessary to "smooth" it (Kaleidograph's word for average). It's intuitive that one should square then average instead of the reverse order. Otherwise there is a cross product,** no? Also it's convenient first to smooth the speed data. Should one smooth the raw (interrupted time) data before inverting, or invert and then smooth? The two do not result in the same value. Of course the difference is very small, as the difference between successive data is very small (otherwise any noise would not be obvious!).Sounds like you are a captive of your measurement method, bc. Another
bc
*** [(speed(n))^2 + (speed(n+1))^2] /2 instead of [speed(n) + speed(n+1} / 2]^2 to obtain the smoothed relative KE. The photogate records the interrupt time, the inverse of which is the relative speed. For calculating Q relative is sufficient, as the coefficients cancel and the photogate need only be near BDC. Curiously, BDC changes as the pendulum decays.