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A single TCP connection with a time varying capacity bottleneck link is considered. The bottleneck capacity varies arbitrarily and independently of the TCP connection traffic; it aims at reproducing typical situations where capacity is modulated by exogenous process, such as wireless channel with link adaptation or bursty channels. The key point is to understand the interplay of the TCP congestion control evolution and the time constants of the bottleneck link capacity time variation. Fluid modeling is used to describe the time evolution of the congestion window size and of the bottleneck buffer content with a completely general capacity time function, ns-2 based simulations are used as mean to assess the fluid model accuracy. Numerical results show the existence of a "resonance" phenomena, that can significantly degrade the TCP long term performance (even more than halved). The degradation depends on the ratio between the fundamental time constant of the link capacity variation and the TCP average round trip time.