Comment on "Slow passage through resonance".

Abstract

In a recent numerical and analytical study, Park et al. [Phys. Rev. E 84, 056604 (2011)PLEEE81539-375510.1103/PhysRevE.84.056604] presented the statement that a linearly damped harmonic oscillator subject to a linear frequency chirp ω_{f}(t)=ω_{0}+εt experiences "an early onset of resonance, setting in when the ramped forcing frequency is midway between its initial value ω_{0} and the natural frequency ω_{n} for resonance in the unforced problem," i.e., the resonance occurs when the instantaneous frequency ω_{inst} approaches (ω_{0}+ω_{n})/2. This statement is not valid because the instantaneous frequency of the forcing function actually grows twice as fast as stated in the paper, and the resonance actually occurs for instantaneous forcing frequency ω_{inst} approximately equal to the natural frequency ω_{n}. We also highlight the difference between the critical frequency ramp rate for resonance amplitude measurement and the critical frequency ramp rate for resonance frequency and damping measurements.