Pendulums and the Passing of Time

In Part 3 of the experiment you generated a graph of Period Vs. Length of a pendulum. If you completed this correctly, you should have produced a graph of a parabola with a vertex at the point (0,0) and opening to the right. This suggests a mathematical relationship of the format

y² = k x. To verify this relationship, a fourth graph will be plotted of (Period)² Vs. Length.

Calculations: In order to draw the fourth graph for this experiment it will be necessary to calculate the square of the period (that is the period squared, or T²). This can be done by either multiplying the period by itself, or using the x² button on you calculator. Enter the square of the period in your data table.

Graph: Plot a graph of (Period)² Vs. Length for the pendulum. If appropriate draw a line that best fits the data.

Analysis of

graphs: In your formal lab report include an analysis for each of the graphs that you constructed. For each graph, write a paragraph describing the shape of the graph. Discuss the relationship of the two variables (i.e. as one variable increases the other ________ ). Is the graph linear or is it a curve? If it is a curve, what type of curve? What mathematical relationship is suggested by the graph? Attempt to write a mathematical equation for the graph and show how the two variables measured fit into that equation. Finally, identify any data points that seem to be in error, that is if they do not "fit" the general pattern of the graph.