3A70.u3 - Bi-Frequency Pendulum
Demonstrate Second Harmonic Generation and Parametric Excitations.
Disturb the pendulum bob in a single direction from its initial equillibrium position and release it. Watch as the energy transfers from one axis to another and back again over time.
Second Harmonic generation and Parametric Excitations require phase-matching, central symmetry violation, and other tunings.
Proper choice of relationships betweens stick's length h, string length L, and tilt (theta) allows to tune the frequency ratio 2 to 1 for the two linearized eigenmodes. w1 = (g*cos(theta)/(h+L*cos(theta)))^(1/2), and w2 = (g/L)^(1/2).
The Non-Linear aspects have great teaching significance for difficult subjects in the field of optics being analogous to the electron mapping in a medium with passing electromagnetic waves.