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Grandfather's Clock - Nonlinear Pendulum

  1. Dec 4, 2007 #1
    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/[tex]\sqrt{2E-q^2 - \epsilon/2*q^4}[/tex]
    where q is position
    E= 1/2 (q'^2 + q^2) + [tex]\epsilon/4 * q^4[/tex]

    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.

  2. jcsd
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