What is the formula of ring difference method in high school physics

It's the difference by difference method
For example, for the paper tape produced by the dot timer, the displacement of each equal period of time from small to large is S1, S2, S3, S4,
Even number of data should be used in the successive difference method. If s1-s8 is taken, then
Formula: ⊿ s = [(s8-s4) + (s7-s3) + (s6-s2) + (s5-s1)] / 16
Note: because there are four ⊿ s in each bracket, there are four brackets in total, so it is divided by 16
If S1-S6 is chosen, then
Formula: ⊿ s = [(s6-s3) + (s5-s2) + (S4-S1)] / 9

How to deduce the formula of successive difference method

According to the fact that the displacement difference in the adjacent equal time interval of the uniform velocity linear motion is equal, we can know that Δ s = at ^ 2. In order to reduce the error, we need to take the farther point to calculate. From the formula, we can deduce that S4-S1 = 3 Δ s = 3At ^ 2 / x0d, so A1 = (S4-S1) / 3T ^ 2 / x0d is the same as A2 = (s5-s2) / 3T ^ 2 / x0da3 = (s6-s3) / 3T ^ 2 / x0d. the purpose of multiple calculations is to take the average value to reduce the error. Generally speaking, three are enough, Then take the average of the three average values to get the acceleration calculated by the successive difference method

Derivation process of formula of successive difference method for measuring acceleration

Such a problem is generally to give a strip of paper and select it from the relatively clear points. Every five points is a counting point. In this way, the time interval between each counting point is Δ t = 0.1s. Generally, about seven points are selected. The first point is marked as o point. The distance between adjacent two points is measured as S1, S2 S6 according to uniform speed change

What is the formula of ring difference method in high school physics