The nonlinear vibrations of the spring doorstop.

The sonorous twang of the spring doorstop is known and beloved throughout the United States. The waveform consists of a series of impulses of partly random character with significant spectral energy up to 8 kHz. The inverse of the impulse spacing is the fundamental frequency and the waveform exhibits well-developed harmonics at least up to the 20th. Two polarizations of spring vibrations may be excited, but there is a preferred orientation. As the doorstop vibration decays the polarization rotates into the preferred orientation. The fundamental frequency rises by more than an octave (16 to 40 Hz is typical). The fundamental frequency increases linearly with the number of cycles therefore it increases exponentially with time. Stroboscopic observation reveals no indication of wave motion along the spring axis. Therefore it is possible to model the system as two coupled, damped oscillators. The nonlinearity presumably arises from the compression of the spring, which produces a force discontinuity at the origin. Numerical solution of the coupled nonlinear differential equations reproduces most of the features of the spring vibrations, but as of this writing the computed frequency increase with increasing cycle number is not linear, as observed experimentally, but has positive curvature. [ABSTRACT FROM AUTHOR]