Abstract: 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.

Key words: theoretical mechanics, Lagrange equation, precession, elastic rod