# Grandfather's Clock - Nonlinear Pendulum

1. Dec 4, 2007

### m0nk3y

1. The problem statement, all variables and given/known data
A Grandfather's Clock is adjusted to keep perfect time if the amplitude is 2 degrees. How many seconds does it lose or gain in a year if instead the amplitude is 10 degrees.

2. Relevant equations
T/4 = integral from 0 to qmax = dq/$$\sqrt{2E-q^2 - \epsilon/2*q^4}$$
where q is position
E= 1/2 (q'^2 + q^2) + $$\epsilon/4 * q^4$$

3. The attempt at a solution

I started by converting 2 degrees and 10 degrees into radians and, then I took the difference I got 2*pi/45 , and made the integral from 0 to 2*pi/45 since we want to get the time difference between these angles, but I don't know where to go from here, and I don't know if what I did was right.

Thanks