为研究支撑杆为弹性杆时单摆的轴向振荡和切向振荡相互转化这一现象，本文提出基于保守系拉格朗日方程的理论与实验探究方法.分析摆球在不同初始释放角，不同摆线长度以及不同杨氏模量的支撑杆的条件下，在两个垂直方向上振荡的转化时间，以及摆球轨迹和分位移的改变情况.理论与实验结果表明初始释放角越大，转化时间越短; 摆长越短，转化时间越短; 支撑杆杨氏模量越小，转化时间越短.实验数据与理论结果吻合良好，从理论上很好地解释了实验现象.

In order to study the mutual transformation of the axial and tangential oscillations for

a simple pen- dulum when the support rod is an elastic rod，we propose a theoretical and

experimental method based on the con- servative Lagrangian equation and analyze the transformation

time of the pendulum ball oscillating in two vertical di- rections under the conditions of

different initial release angles，cycloid lengths and Young’s modulus support rods， and their

influences on trajectory and sub-displacement of the ball. Both theoretical and experimental

results show that larger initial release angle，shorter pendulum length and smaller Young’s

modulus of the support rod will make the transformation shorter. The experimental result is in

good agreement with the theory，and the theory can explain the experimental phenomenon well.