Abstract
This paper describes a method for finding an approximate solution to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\ddot{\phi} + f(\phi) = 0</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(\phi)</tex> is an odd polynomial. The technique consists of approximating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(\phi)</tex> by an odd cubic, and hence obtaining an approximate solution in the form of a Jacobian elliptic function. The solution is compared to the classical Ritz solution of both one and two terms and is found to be superior. Also, the labor involved in obtaining the solution is considerably less, which makes the method easily applicable to various engineering problems involving the equation under consideration.
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