tokens: / L ≈ 0.02. Similar results were found later by Goddard et al. ( 2016 ) with a large array of SDO data. They performed a statistical study of decaying kink oscillations in 120 coronal loops. The best-fitting results were given. In particular, with the mean period P ≈ 350 s and damping time τ ≈ 535 s, the ratio was found τ/ P ≈ 1.53 or γ/ω ≈ 0.10. The average length of analysed loops is L ≈ 240 Mm. We use the above data and the mean density contrast in oscillating coronal loops χ ≈ 0.3, given by Aschwanden et al. ( 2003 ). The aspect ratio, given above, indicates that the fundamental kink oscillations occur at dimensionless axial wavenumber k n a = π a / L ≈ 0.06. Substituting the mean density contrast in equation ( 32 ) we find that Equation ( 50 ) implies that the cut-off wavenumber exceeds the actual observable axial wavenumber of principal kink mode if the source distance d ≤ 70 a , or in terms of loop length if d ≤ 1.4 L . This is a realistic restriction, as the observable distance between the nearby flare sight or erupted filament and the impacted coronal loops is comparable with the loop length. In this case, the externally excited principal kink mode of coronal loops exists in the leaky regime and it is subjected to damping due to the wave leakage effect. With known oscillation parameters ω, γ/ω, χ and loop length L and semiwidth a , we can consider equations ( 43 ) and ( 45 ) as a system for unknown values V Ae and d . We then obtain the following estimates: V Ae ≈ 1250 km s −1 and d ≈ 0.6 L . 5 CONCLUSIONS We have studied the dispersion properties of fast oscillations in a coronal plasma slab with anchored ends. It is assumed that these oscillations are excited by a finitely distant external source. The coronal slab is considered as an enhancement in plasma density with a discontinuous boundary, embedded within uniform environment. A magnetic field is assumed to be everywhere uniform. Using the Fourier transform, the inhomogeneous boundary value problem was solved to obtain the solutions to wave variables in all the regions of the considered model. Corresponding solutions with known coefficients inside the slab contain the so-called dispersion function D (ω) in their denominators and this function completely governs the properties of the slab eigen-oscillations, excited by the external driver. The results of the study are summarized as follows. Both the kink and sausage modes are excited. There are two sets of zeros of the dispersion function. Each of these systems of roots prescribes both axially asymmetric and axially symmetric oscillations. With the appropriate condition that the distance between the source and the slab axis d is much more than the slab semiwidth a (i.e. d ≫ a ), we have shown that the first set of solutions corresponds to kink oscillations of the slab with finite amplitudes and sausage oscillations with negligible amplitudes, proportional to ∝ δ ∝ exp [− 2 m e ( d − a )] ≪ 1, whereas another set prescribes the
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