PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Nonlinear dynamics and chaos · Nonlinear dynamics and chaos
Modes, Packets and Media, Ch Driven and pumped nonlinear oscillators and the route to chaos
Problem
A driven pendulum, sampled once per drive period (a stroboscopic section), settles into a period-three orbit: the strobe shows exactly three distinct points, and the trajectory exactly repeats after three drive periods. The drive angular frequency is ωd=0.900rad s−1.
((a)) List, in ascending order, the angular frequencies (up to and including ωd) at which this motion can show spectral lines.
((b)) State why a period-three orbit cannot show a line at ωd/2.