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Josephson transmission lines (JTLs) are commonly used as signal interconnects in single-flux quantum (SFQ) circuits. They are also used, however, to transform arbitrary waveforms into SFQ pulses. Here we use a low-temperature electro-optic sampling system with subpicosecond resolution to observe the response of a JTL to a picosecond input pulse. Previously, this system has been used to directly observe SFQ pulses on niobium transmission lines. In our experiment, niobium metal semiconductor-metal (MSM) photodiodes were connected to 3, 4, 19, and 20-stage JTLs. The MSM photodiodes provided picosecond pulses to excite the JTL. The JTL bias and input pulse amplitude were varied to observe fluxon interaction and time delay of the JTL stages. Observed JTL behavior is dominated by dipolar oscillations radiated from the first stages of the JTL. By varying the values of line inductance and junction capacitance, thus changing the oscillation periods, these oscillations were traced to the coupling of the junction capacitance and line inductance. This is a new feature of the JTL that has thus far not been observed or incorporated into simulations. Our results could have significant implications on the limit of SFQ circuits.