We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the natural frequency is sufficiently slow compared to the time period of oscillation. Thanks to such a simple formulation, we found that a forced harmonic oscillator with a slowly varying natural frequency is essentially equivalent to diffraction of light.
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Hiraiwa et al. (2020) studied this question.
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