Handicapped pendulum assignment

[tomkoolen]

"Handicapped" pendulum assignment

Hello everyone,

I was wondering if anyone could help me with an assignment about a "handicapped" pendulum (you got to love the professor's taste for scientific terminology). By "handicapped", it is meant that the pendulum is attached to a stationary point, limiting the pendulum's swinging movement. The assignment is about researching the relation between the height of the stationary point and the period of the pendulum.

It's overall a very easy assignment, but I have two problems with it:
1) I need to prove that T(T stands for period) - 0.5T₀ = ∏√((l-h)/(g)), with T₀ being Huygens' law = 2∏√(l/g). I don't know how I should make a formula for T, seeing as my only resource is some measurement data, namely:

displacement from equilibrium position: 20 cm
length: 97 cm
√(l-h) ---- Period
8.8 1.88
8.2 1.85
7.5 1.76
6.9 1.69
6.1 1.61
5.2 1.54

2) I also have a T', which is the period of a pendulum with a similar stationary point, but this time, it's 5 cm horizontally away from the vertical line of the pendulum. The following measurements were made:

displacement from equilibrium position: 20 cm
length: 97 cm
√(l-h) ----- Period
8.2 1.95
7.5 1.89
7.0 1.81
6.1 1.74
5.2 1.64

These square roots were calculated with h \in [30;70]. I now have to predict the function's behaviour between h = 0 and h = 30.

Anyone with any ideas as to how to solve one or both of these problems, I would be very thankful to hear them.

 

[tomkoolen]

To clarify the height that is meant by h, please check the image:

http://dl.dropbox.com/u/37807450/Schermafbeelding%202013-01-05%20om%2018.27.26.png

 

[haruspex]

The plot should be a straight line, right? So plot the data and compute the R value, slope, etc.

 

[tomkoolen]

The plot should be a straight line, right? So plot the data and compute the R value, slope, etc.

Thank you very much!