The Swinging Spring : A Simple

Pulsation and Precession of the Resonant Swinging Spring

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as pulsation. Between the horizontal excursions, or pulses, the spring undergoes a change of azimuth which we call the precession angle. The pulsation and stepw...

Stepwise Pre ession of the Resonant Swinging Spring

Stepwise Precession of the Resonant Swinging Spring

The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the wellknown three-wave equations that also apply, for example, in laser-matter interaction in a cavity. We use Hamiltonian reduction and pattern evocation techniques to derive a formula that describes the characteristic feature of thi...

Resonators in Insect Sound Production : How Insects Produce Loud Pure - Tone Songs

songs of insects may be shrill, raucous or musical, brief or sustained but, whether loud or quiet, they tend to convey information within a narrow band of sound frequencies. The narrow frequency band implies that the sound-producing system is in some way tuned. In this review, I shall address the mechanisms by which sharply tuned sounds are produced by insects and explore the acoustical and bio...

Resonant Rossby Wave Triads and the Swinging Spring

From page xxxx) The wave solutions discovered by Rossby are of fundamental importance for atmospheric dynamics. The nonlinear interactions between these waves determine the primary characteristics of the energy spectrum. These interactions take place between triplets of waves known as “resonant triads” and, for small amplitude, they are described by the three-wave equations. These same equation...