Herbert Goldstein, 'Classical Mechanics', says the the pendulum at the North pole and elsewhere on the earth's surface act qualitatively similar, but the details are a bit different and and are left to the reader (student) as an exercise. That exercise is the last (and undoubtably hardest) problem at the end of the chapter. I don't think I ever tackled it, and I have the student's edition of the book, without the answers to any problems. So work it out yourself, or go to www.bibliofind.com and try to get the instructor's edition with the answers (and check that the answer to problem 12, chapter 4 is there before you buy it).