Question

Fill the table with the provided data and plot a graph according to steps 7 and 9.30 cmTrial 1: 1.09sTrial 2: 1.09sTrial 3: 1.09s50cmTrial 1: 1.42sTrial 2: 1.39sTrial 3: 1.42s70cmTrial 1: 1.66sTrial 2: 1.66sTrial 3: 1.66s

Answer 1

First, fill the first column with the length of the string of the different pendulums:

`\begin{gathered} \text{ Length of string \lparen}m\text{\rparen} \\ 0.30 \\ 0.50 \\ 0.70 \end{gathered}`

Fill the next three columns of each row according to the time obtained using the simulator:

`\begin{matrix}\text{ Length of String \lparen}m\text{\rparen} & \text{ Period 1 \lparen}s\text{\rparen} & \text{ Period 2 \lparen}s) & \text{ Period 3 \lparen}s\text{\rparen} \\ 0.30 & 1.09 & 1.09 & 1.09 \\ 0.50 & 1.42 & 1.39 & 1.42 \\ 0.70 & 1.66 & 1.66 & 1.66\end{matrix}`

Take te average of the period for each row in order to obtain the data for the column Average Period:

`\begin{gathered} 30cm: \\ \\ (1.09+1.09+1.09)/(3)=1.09 \\ \\ \\ 50cm: \\ \\ (1.42+1.39+1.42)/(3)=1.41 \\ \\ \\ 70cm: \\ \\ (1.66+1.66+1.66)/(3)=1.66 \end{gathered}`

Then, the fifth column is:

`\begin{gathered} \text{ Average period \lparen}s\text{\rparen} \\ 1.09 \\ 1.41 \\ 1.66 \end{gathered}`

Square the values of the fifth column to fill the sixth column:

`\begin{gathered} 1.09^2=1.1881 \\ 1.41^2=1.9881 \\ 1.66^2=2.7556 \end{gathered}`

Then, the fourth column is:

`\begin{gathered} \text{ Square of average period \lparen}s\text{\rparen} \\ 1.1881 \\ 1.9881 \\ 2.7556 \end{gathered}`

Use a graphing facility to find the best fit line for each data set (average period vs length and square of average period vs length):