The figure shows a pendulum with length L that makes a maximum angle theta0 with

Question

The figure shows a pendulum with length L that makes a maximum angle theta0 with the vertical. Using Newton's Second Law it can be shown that the period T (the time for one complete swing) is given by the following where k = sin((l/2)theta0) and g is the acceleration due to gravity. If L = 1 m and theta0 = 44degree, use Simpson's Rule with n = 10 to find the period. (Note: Intermediate rounding can cause your answers to be quite far off. To be safe, if you round any intermediate values do not round them to any less than 10 decimal places (if possible). Give your final answer correct to at least 2 decimal places.)

Explanation / Answer

No, the period is given by
Pendulum period in seconds
T 2(L/g)
L is length of pendulum in meters
g is gravitational acceleration = 9.8 m/s²

But this has errors for large angles. You can use one of the formulae below for a more accurate number.
Pendulum period in seconds for larger angle, in radians
T [2(L/G)] [1 + (1/16)² + (11/3071) +
(173/737280) + (22931/1321205760) + ... ]
T [2(L/G)] [1 + (1/2)²(sin²(/2) +
((1·3)/(2·4))²(sin(/2) +
((1·3·5)/(2·4·6))²(sin(/2) + .. ]

Simpson's rule is a method for numerically evaluating an integral:

where n is the number of divisions, h=(b-a)/n, and xi=a+ih. This problem is pretty much just plugging everything into the formula and grinding out an answer.

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