Rotation of the Oscillation Plane of a Heavy Mass Point on a Spring in Resonance

摘要

Nonlinear spatial oscillations of a swinging spring in the 1: 1: 2 resonance are considered. Numerical calculations and experiments show that the oscillations along the vertical are unstable in this case, which leads to periodic pumping of the energy of vertical oscillations into the energy of horizontal oscillations and vice versa. Pendulum oscillations along the vertical are stopped, and the pendulum starts to perform horizontal oscillations in a certain vertical plane. Then the energy is pumped into the vertical mode and oscillations along the vertical are repeated. After the second energy pumping into the horizontal mode, the oscillation plane is rotated to a certain angle. In this study, we derived an analytical formula for the rotation angle of the oscillation plane. The analytical dependence of the rotation angle agrees with numerical calculations performed with a high accuracy.