The demonstrations begin with a mass suspended from a spring, which is used in the video “Period of Simple Harmonic Motion.”
The original 1.0 kg mass is then replaced with a 0.5 kg mass, and the longitudinal oscillations are now observed to be unstable when the amplitude exceeds a threshold value.
This remarkable behavior is due to the phenomenon of parametric excitation, which is explained and demonstrated in the video “Parametric Excitation.”
The instability of the mass-and-spring system is explained as an internal parametric excitation, where the longitudinal mode parametrically drives a transverse mode.
This effect can occur for ships at sea, where waves excite vertical oscillations which then parametrically drive rocking oscillations. Substantial damage has been caused due to this effect!
Finally, internal parametric excitation is exhibited in the normal modes of a system of two coupled pendulums.
A journal article can be found here.
drive.google.com/open?id=17W_...
Supports the following NPS courses: PH3119 (Oscillation and Waves), PH3451 (Fundamental Acoustics), PH4454 (Sonar Transduction).