# Pendulum Experiment - Finding relationship between period and length

Tags: experiment, length, pendulum, period, relationship
 P: 76 In my physics class we did an experiment where we timed the oscillations of a lead bob when swung from a small angular displacement and were asked to find the relationship between oscillation time (period) and string length. We were given 4 possible equations and asked to find the right one and I know it is this one "T2 = Al" because the teacher told us but I'm completely lost. Heres some of my results taken Length/m---------Time for 30 oscillations /s 85-----------56.4 72-----------81.9 63-----------48.2 52------------43.9 36-----------36.8 A in the formula was defined as 4pi2/g. We were told to "Examine the data and select the relationship that best fits the experimental data. Plot the appropriate graph of the quantities involved. A straight line graph through the origin confirms that you have selected the appropriate relationship." I'm not quite sure what values to plot this graph with. I tried drawing a graph with T2 as X and Al as Y but I don't know what the origin he's talking about is. I have to write a report on this experiment but I dont really know whats going on so Im stuck.
P: 112
 I tried drawing a graph with T2 as X and Al as Y...
Yes, that's right! Since T2 = Al, a plot of T2 against Al will yield a straight line of gradient m = 1 and passing through the origin. (The "origin" is just another name for the point (0,0).)

Now, because all you need to do is prove that the string length is proportional to the period squared (lT2) you only need plot T2 against l. You don't need to multiply l by A to prove this linear relationship. A is just a coefficient.

One more point: I'm not sure whether it is considered a "rule" or a convention, or simply a matter of personal preference, but I believe that in this case it would be most usual to plot l along the x-axis and T2 along the y-axis -- not the other way around. I was taught to place the dependent variable along the x, that's all. Someone else can tell you if that really is the rule.

- m.e.t.a.