Stationary and transient resonant response of a spring pendulum

摘要

Plane motion of the spring pendulum is considered. The mathematical model of the system is transformed into dimensionless complex form and then the analytic approach using multiple time scale method is applied to solve the obtained initial value problem. The approximate analytical solution gives possibility to analyse steady-state and transient motion of the system for various parameters. Especially non stationary processes are discussed. The nonlinear transition of the dynamics and intersections of the tori are presented. For steady-state vibration the frequency response functions are derived. All analytical results are fully confirmed by numerical analysis.