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Re: Spreadsheet Analysis of Rotating Stick



On Sun, 28 Nov 1999, Robert Carlson wrote:

Here is a question for anyone on the list. What is the period of a point
mass attached to a string of length one meter, released from rest from the
horizontal?

The small angle approximation gives 2.01 s which is of course not correct
here. In Tipler, an approximation for T is given as:

T = To(1+ 0.25sin(0.5B)^2+0.1406sin(0.5B)^4+ . . .)

Where To = 2.01 s, and B is the release angle measured from the vertical of
the bob at its lowest point.

For B = 90 degrees this gives T = 2.33 s. However, this only includes terms
through sin(0.5B) to the fourth power.

The spreadsheet gives T = 2.37 s.

For an initial angle of 90 degrees, the series becomes

1^2 1 1^2 * 3^2 1
T = To(1 + --- * --- + --------- * --- + ... )
2^2 2^1 2^2 * 4^2 2^2

= To(1.1803406...)

So, for L = 1 m and g = 9.8 m/s^2 T = 2.36904972... s in agreement with
your spreadsheet solution.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm