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Transverse Coronal-Loop Oscillations Induced by the Non-radial Eruption of a Magnetic Flux Rope

We investigate the transverse coronal-loop oscillations induced by the eruption of a prominence-carrying flux rope on 7 December 2012. The flux rope originating from NOAA Active Region (AR) 11621 was observed in EUV wavelengths by the SDO/AIA and in H$α$ line center by the ground-based telescope at the BBSO. The early evolution of the flux rope is divided into two steps: a slow rise phase at a speed of $\approx$230\,km\,s$^{-1}$ and a fast rise phase at a speed of $\approx$706\,km\,s$^{-1}$. The eruption generates a C5.8 flare and the onset of the fast rise is consistent with the HXR peak time of the flare. The embedded prominence has a lower speed of $\approx$452\,km\,s$^{-1}$. During the early eruption of the flux rope, the nearby coronal loops are disturbed and experience independent kink-mode oscillations in the horizontal and vertical directions. The oscillation in the horizontal direction has an initial amplitude of $\approx$3.1\,Mm, a period of $\approx$294\,seconds, and a damping time of $\approx$645\,seconds. It is most striking in 171\,Å and lasts for three to four cycles. The oscillations in the vertical directions are observed mainly in 171, 193, and 211\,Å. The initial amplitudes lie in the range of 3.4\,--\,5.2\,Mm, with an average value of 4.5\,Mm. The periods are between 407\,seconds and 441\,seconds, with an average value of 423\,seconds. The oscillations are damping and last for nearly four cycles. The damping times lie in the range of 570\,--\,1012\,seconds, with an average value of 741\,seconds. Assuming a semi-circular shape of the vertically oscillating loops, we calculate the loop lengths according to their heights. Using the observed periods, we carry out coronal seismology and estimate the internal Alfvén speeds (988\,--\,1145\,km\,s$^{-1}$) and the magnetic-field strengths (12\,--\,43\,G) of the oscillating loops.