论文标题
解决简单谐波运动的新颖方法
Novel Approaches to Solve Simple Harmonic Motion
论文作者
论文摘要
本文提出了两种新的方法来解决经典的简单谐波运动。在一种方法中，平衡位置与最大位移之间的距离分为N相等的段。在每个段中，质量在段末端的两个力的平均值下以恒定加速度移动。总结覆盖每个细分市场的时间并采取大N限制重现该期间的四分之一，以进行简单的谐波运动。在另一种方法中，从最大位移到平衡位置的时间分为n相等的间隔。获得位移的复发关系。其溶液的大N极限导致与求解微分方程获得的溶液相同。
This paper presents two novel approaches to solve the classic simple harmonic motion. In one approach, the distance between the equilibrium position and the maximal displacement is divided into N equal segments. In each segment, the mass moves with constant acceleration under the average of two forces at the ends of the segment. Summing up the time covering each segment and taking the large-N limit reproduce one quarter of the period for simple harmonic motion. In the other approach, the time moving from the maximal displacement to the equilibrium position is divided into N equal intervals. A recurrence relation for the displacement is obtained. The large-N limit of its solution results in the same solution as that obtained from solving differential equation.
