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 [itex]\in[/itex] [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!

 

[Nickie]

Thank you for your question and for sharing your assignment. It seems like you have a good understanding of the concept of a "handicapped" pendulum and the purpose of the assignment.

To address your first problem, it looks like you have all the necessary data to create a graph of T versus √(l-h). From there, you can use the graph to estimate the value of T for different values of √(l-h). Once you have those values, you can plug them into the equation T(T stands for period) - 0.5T0 = ∏√((l-h)/(g)) and see if they match up. If they do, then you have successfully proven the relationship between T and √(l-h). If not, you may need to check your calculations or data to see if there are any errors.

For your second problem, it seems like you are being asked to predict the behavior of T' for values of h between 0 and 30. One approach could be to create a graph of T' versus h and see if there is a clear trend or pattern. From there, you can use that trend to predict the behavior of T' for values of h between 0 and 30. Another approach could be to use the equation T(T stands for period) - 0.5T0 = ∏√((l-h)/(g)) and plug in different values of h to see how T' changes.

I hope these suggestions are helpful in solving your assignment. If you have any further questions or need clarification, please don't hesitate to ask. Good luck!