Pendulum Experiment - Finding relationship between period and length

[MadmanMurray]

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 don't really know what's going on so I am stuck.

 

[m.e.t.a.]

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 (l ∝ T²) 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.

 

[Vanadium 50]

Meta gives you some good advice.

At the risk of sounding like a grumpy old man, let me tell you that if you claimed that your data tells you that you have confirmed that the period is proportional to the square root of the length, I would flunk you.

Your data doesn't fit the curve T² = kL very well. It doesn't fit the curve T = kL very well either. Because of that, you cannot say that your data supports one over the other. In lab, it is very important that you report on the observations you actually made, not on your expectations of what you should have measured. It is far, far worse to draw conclusions based on expectations instead of data than to have made some bad measurements. Bad measurements are just bad measurements, and with experience, one stops making them. But when you start drawing conclusions based on expectations instead of measurements, you have left the realm of science.

Two other points: one is "are you sure the length of the string is in meters?" Did you really have an 85m long string? This is also a critical part of the reason we teach labs - so students will learn to ask themselves "do the numbers make sense?"

The other is that your 72m point is longer than both the 63m and 85m points. Does this make sense? Are you sure this point is accurate? When you were taking this data, did you notice this?

 

[m.e.t.a.]

In lab, it is very important that you report on the observations you actually made, not on your expectations of what you should have measured.

Very true. Murray, consider yourself lucky -- Vanadium has pointed out some important flaws in your results, which you can now learn from. Take his advice and always leave your experimental results unchanged. By all means change "metres" to "centimetres" if all you are doing is correcting a typo. But as for your results, keep them just as they are, and show your teacher that you know how to identify and handle erroneous results.

Also, I should have pointed out that the linear relationship between l and T² is only a good approximation when the pendulum displacement angle is small. So even if all of your period measurements were extremely accurate your graph would still not show a perfectly straight line.

 

[flatmaster]

I agree with Vanagrum in that you should write you lab as interpurting your result, rather than expectations. However, if you can't find the correct data for the 72cm trial, I would throw this data point out. Although you are taking conclusions from your data, it is alright to remove data that was obviously taken in error.