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# TI-83 with the Pendulum Lab

## Graphing the Pendulum Period

1. Clear any equations in the equation editor:   Y=   . Delete each function using the arrow keys and   DEL   .
2. Clear the statistics lists:   2ND     +     4     ENTER
3. Enter the string length (in meters) data as L1:   STAT     1   .
4. Enter the period (secs) data as L2. A set of sample data is shown to the right.
5. Select a statistics scatter plot:   2ND     Y=     1  .
1. Press   ENTER   when the cursor is highlighting "On".
2. Use the arrow keys to select the Type: scatter graph.
3. XList:L1 and YList:L2 should select automagically.
4. If not, use the arrow keys and ALPHA   1   and   2   to select L1 and L2.
5. A properly configured screen shot is at the right.

6. Set the optimum stat plot graphing window:   ZOOM     9   .
7. The data should be displayed. The user can use   TRACE     to examine data points.

## Modeling the Length / Period Relationship

The TI-83 can find a mathematical equation that models the pendulum system data you have gathered.

1. Turn on a useful diagnostic:   2ND     0     X -1   .
2. Use the arrow key to scroll down to DiagnosticOn. Press   ENTER     ENTER
3. Enter the pendulum data as described above in steps 1 through 3. 4. Press   STAT   and arrow right to CALC.
5. Arrow down to option A: PwrReg. Press   ENTER     ENTER
6. A typical equation display screen is shown at the right.
7. The equation that best fits the set of sample data in this case is Y=2.22 X .53
8. The closer r is equal to 1 the better the equation 'fits' the data. The r=.99 shown here means the equation is a very good fit to the data.

## Graphing the Ideal Length / Period Relationship

It is interesting to compare the ideal mathematical model to the actual data. The ideal equation is Y=2 X.5

1. Enter the ideal equation into the equation editor.   Y =
2. Y1=2*X^.5
3. Use   GRAPH     to view your data and the ideal equation.