We for the first time obtain the analytical solution for the quirk equation of motion in an approximate way. Based on it, we study several features of quirk trajectory in a more precise way, including quirk oscillation amplitude, number of periods, as well as the thickness of quirk pair plane. Moreover, we find an exceptional case where the quirk crosses at least one of the tracking layers repeatedly. Finally, we consider the effects of ionization energy loss and fixed direction of infracolor string for a few existing searches.
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