Polynomial expression of Pendulum period with respect to angle (large)

1. Aug 12, 2011

seboastien

1. The problem statement, all variables and given/known data

The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude period can be expressed as an even polynomial in initial angle θ. Find T(θ) for large amplitude pendulum

2. Relevant equations

Some even polynomial

3. The attempt at a solution

I assume that The function takes the form, T(θ) = (2pi*sqrt(l/g))(1+aθ^2 + bθ4 + cθ^6+....)
Where a,b,c..... are constants. But I have no way of proving this, nor do I know how to find out what these constants are!! Help!!

2. Aug 12, 2011