Mechanical resonance Mechanical resonance Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its "resonance frequency" or "resonant frequency") than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings and airplanes. This is a phenomenon known as resonance disaster. Avoiding resonance disasters is a major concern in every building, tower and bridge construction project. The Taipei 101 building relies on a 660-ton pendulum—a tuned mass damper—to modify the response at resonance.
Tune shift with amplitude case with distributed sextupoles, one can see anharmonicity Tune shift with amplitude The tune shift with amplitude is an important concept in circular accelerators or synchrotrons. The machine may be described via a symplectic one turn map at each position, which may be thought of as the Poincaire section of the dynamics. A simple harmonic oscillator has a constant tune for all initial positions in phase space. Adding some non-linearity results in a variation of the tune with amplitude. Amplitude may refer to either the initial position, or more formally, the initial action of the particle. Consider dynamics in phase