- #1

tomkoolen

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**"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) - 0.5T

_{0}= ∏√((l-h)/(g)), with T

_{0}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.