Dynamics of an oscillating chain consisting of several magnetic microparticles and driven by oscillating magnetic fields with different frequencies are discussed. Because of a shorter driving time by the external field with a higher field frequency, the oscillating amplitude of the chain reduces. On the other hand, the higher field frequency leads to a faster local angular velocity. These two effects result in inconsistent behavior of the structural stability of the chain, so that the chain ruptures in a field of intermediate frequency. A dimensionless parameter of the reduced frequency is proposed to generally describe the monotonic decrease of the normalized amplitude. The phenomenon of trajectory shift triggered by the higher frequency field is also demonstrated.