Generalization of the Concept of Bandwidth

In the sciences and engineering, concept of bandwidth is often subject to interpretation depending upon context requirements a specific community. The focus this work formulate for general class passive oscillatory dynamical systems, including but not limited mechanical, structural, acoustic, electrical, optical. Typically, these systems determined by half-power (-3 dB) method, result referred as bandwidth. fundamental assumption underlying definition that system performance degrades once its power decreases 50%; moreover, there are restrictive conditions rarely met. Here root mean square considered, justified Fourier uncertainty principle, generalize encompass linear nonlinear, single multi-mode, low high loss time-varying invariant oscillating systems. By tying an directly dissipative capacity, one can based solely on transient energy evolution, effectively circumventing previous restrictions. Further, applications given highlight limitations traditional bandwidth; Duffing oscillator with hardening nonlinearity, geometrically nonlinear tunable or softening nonlinearity. resulting energy-dependent computations compatible dynamics since at energies they recover bandwidth, whereas accurately capture physics. Moreover, computation tied harmonic generation in dynamics.