The dynamics of an oblate fluid drop is considered in the report. The drop is suspended in a different fluid and confined by two parallel rigid plates. The external vibration force acts on the system. The vibration axis is perpendicular to the symmetry axis of the drop. The both vibration amplitude and drop's height are small in comparison with the drop's radius. Arbitrary values of equilibrium contact angle are considered. The specific boundary condition is applied to take the dynamics of contact line into account: the contact line's velocity is proportional to the deviation of contact angle. It is found that there exist three different levels of natural frequencies. The highest frequencies have oscillations with a wavelength proportional to the height. For such oscillations the contact line is fixed. The lowest frequencies are vibrations with a wavelength proportional to the radius. In this case, the contact line moves freely along the solid surfaces. Average frequency oscillations have a wavelength which is proportional to the constant Hocking. Such movement corresponds to the translational vibration mode, which describes the movement of the center of mass of the drop. It is found that for finite values of capillary parameters of motion of the contact line leads to damping of free oscillations. The effect of dissipation leads to a limitation of the maximum amplitude at the resonance and to the shift of the resonant frequency. The largest amplitude of forced vibrations is achieved in the case of a direct equilibrium contact angle
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