本論文運用微分轉換法求解非線性系統振動的問題。文中首先介紹微分轉換理論的定義、性質及其基本演算。運用微分轉換方法將自由振動的非線性微分方程式轉換為差分方程式，這組差分方程式經由代數運算求解，最後以迭代方式可求得原微分方程式的解。論文內針對幾組不同的參數和初始條件，以微分轉換分別求得各別的結果並與 Runge-Kutta 方法計算的結果作比較。經由比較運算的結果，可以得知在求解非線性微分方程式上，微分轉換方法是一種準確而有效率的方法。

This paper adopts the differential transformation method to solve the free vibration behavior of an oscillator with cubic or fifth non-linearities. The principle of differential transformation is briefly introduced, and is then applied in the derivation of a set of difference equations for the free vibration oscillator problem. The solutions are subsequently solved by a process of inverse transformation. The time responses of the oscillator are presented under different parameter conditions, and the current results are then compared with those derived from the established Runge-Kutta method in order to verify the accuracy of the proposed method. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the proposed differential transformation method is a powerful and efficient tool for solving non-linear problems.

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