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.

• Received 27 April 2020
• Revised 14 July 2020
• Accepted 22 August 2020

DOI:https://doi.org/10.1103/PhysRevE.102.032211