Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Negative frequency is just a constant whose amplitude level is a measure of the strength of the original "ω" content. And whatever part of "x"("t") that was at frequency zero is changed to a sinusoid at frequency −"ω". Similarly, all other frequencies are changed to non-zero values. As the interval increases, the contribution of the constant term grows in proportion. But the contributions of the sinusoidal terms only oscillate around zero. So "X"("ω") improves as a relative measure of the amount of frequency "ω" in the function "x"("t"). The Fourier transform of formula_1 produces a non-zero response only at frequency "ω". The