OscillayneThe Harmonic Pulse / Waveform Resonance

Oscillayne does not push hard. She pushes on time.

Anything that can wobble has a natural frequency: a swing, a wine glass, a bridge deck, the quartz crystal in a watch. The first formula on this page is the standard model of driving one. A mass on a spring, a friction term γ that drains energy, and an outside force pushing back and forth at frequency ω. Wait for the starting jitters to die away and the system settles into moving at the driving frequency, whatever its own preference.

How far it moves is the second formula. Push far below the natural frequency \(\omega_0\) and it simply follows the force, as if only the spring mattered. Push far above and it barely responds, because the mass cannot keep up. Push near \(\omega_0\) and the first term under the square root nearly vanishes, leaving only friction to limit the motion. There the amplitude exceeds the slow-push response by a factor \(\omega_0/\gamma\), called the quality factor Q. Low-friction oscillators can have a Q in the thousands or far more; a watch's quartz crystal is one, which is why it keeps such steady time.

Resonance also gets blamed for things it did not do. The Tacoma Narrows Bridge tore itself apart in a steady wind on 7 November 1940, four months after it opened, and textbooks long called that resonance. It was not, as K. Yusuf Billah and Robert Scanlan argued in 1991: a steady wind is not a rhythmic push at the bridge's natural frequency. The twisting deck shaped the airflow around it, and the airflow fed the twisting, a self-excited instability engineers call flutter. Resonance needs a rhythm supplied from outside. Flutter makes its own.

Oscillayne waits for the beat. Then she adds a little to it, every time.