We study the magnetization dynamics of coupled vortices in arrays of Permalloy disks via analytical calculations and scanning transmission x-ray microscopy. The Thiele approach is used to derive linear equations of motion of the vortices. Thereby, vortex motions following a nanosecond field pulse are described by a superposition of eigenmodes that depend on the vortex polarizations. Eigenmodes are calculated for a specific polarization pattern of a 3 x 3 vortex array. With magnetic field pulses distinct oscillations are excited and imaged in space and time. The calculated eigenmodes precisely describe the measured oscillations. (C) 2014 AIP Publishing LLC.