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The time-dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds numbers of 200 and 855 was analyzed using a finite volume method. The Navier-Stokes equations were solved on a moving grid system using a time-dependent coordinate transformation. Several numerical schemes were tested to investigate the vortex-shedding characteristics and the effects of Reynolds number and other dimensionless parameters such as the reduced amplitude and the reduced frequency. The numerical results indicate that several types of vortex shedding modes depend on the reduced frequency and the reduced amplitude due to synchronization or lock-on.