Time t yı y2 Уз y4 ys y d (s) (m) (m) (s³) (m) (m) (m) (m) (m) 0.50 0.9 1.3 1.1 1.5 1.4 0.75 3.2 2.7 2.5 2.9 3.0 1.00 4.6 4.6 5.0 4.8 4.8 1.25 7.9 8.0 7.6 7.9 7.6

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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How do we solve for d and y and the other one to fill in the table. 

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**Case 2: Quantification of Random Error: Standard Deviation**

The data table shows results from a free-fall experiment. Compute the mean, absolute deviation in the mean (AVEDEV in Excel), and standard deviation (STDEV) for each of the measurements.

**Instructions:**

**a.** Plot \(\bar{y}\) vs. \(t\) with the error bars from the calculations in the table. Fit the proper curve to the data. (Is it linear or a polynomial?) Galileo determined the relation between the distance of fall and the time to be \(y=\frac{1}{2}gt^2\) where \(g\) is the acceleration due to gravity. This is a second-order polynomial and the equation of a parabola.

**b.** Transform the non-linear plot in part (a) to a straight line by plotting \(\bar{y}\) vs. \(t^2\). Calculate the slope of the line and find \(g\), the acceleration due to gravity. Record your answer on the graph.

**Data Table:**

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
\text{Time } t & y_1 & y_2 & y_3 & y_4 & y_5 & \bar{y} & \bar{d} & \sigma & t^2 \\
(\text{s}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{s}^2) \\
\hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0.50 & 0.9 & 1.3 & 1.1 & 1.5 & 1.4 & 1.4 & & & \\
0.75 & 3.2 & 2.7 & 2.5 & 2.9 & 3.0 & 3.0 & & & \\
1.00 & 4.6 & 4.6 & 5.0 & 4.6 & 4.8
Transcribed Image Text:**Case 2: Quantification of Random Error: Standard Deviation** The data table shows results from a free-fall experiment. Compute the mean, absolute deviation in the mean (AVEDEV in Excel), and standard deviation (STDEV) for each of the measurements. **Instructions:** **a.** Plot \(\bar{y}\) vs. \(t\) with the error bars from the calculations in the table. Fit the proper curve to the data. (Is it linear or a polynomial?) Galileo determined the relation between the distance of fall and the time to be \(y=\frac{1}{2}gt^2\) where \(g\) is the acceleration due to gravity. This is a second-order polynomial and the equation of a parabola. **b.** Transform the non-linear plot in part (a) to a straight line by plotting \(\bar{y}\) vs. \(t^2\). Calculate the slope of the line and find \(g\), the acceleration due to gravity. Record your answer on the graph. **Data Table:** \[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \text{Time } t & y_1 & y_2 & y_3 & y_4 & y_5 & \bar{y} & \bar{d} & \sigma & t^2 \\ (\text{s}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{m}) & (\text{s}^2) \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0.50 & 0.9 & 1.3 & 1.1 & 1.5 & 1.4 & 1.4 & & & \\ 0.75 & 3.2 & 2.7 & 2.5 & 2.9 & 3.0 & 3.0 & & & \\ 1.00 & 4.6 & 4.6 & 5.0 & 4.6 & 4.8
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