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
Amplitude modulation The vacuum tube was responsible for the rise of AM radio broadcasting around 1920, the first electronic mass entertainment medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War 2. At the same time as AM radio began, telephone companies such as AT&T were developing the other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called "frequency division multiplexing". John Renshaw Carson in 1915 did the first mathematical analysis of amplitude modulation, showing that a signal and carrier frequency combined