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An inductor and a capacitor when connected together make a tuned circuit. This sort of circuit resonates at its tuned frequency. This means that any energy that is fed into it will run around in one direction then the other and decay by 1/Q after every cycle. Like a struck gong or cymbal the energy just dies away slowly.
If you apply a pulse with a sharp edge and a low repetition frequency, it will contain a whole host of frequencies and if one of these hit the resonant frequency the tuned circuit is tuned to the tuned circuit will produce a damped sine wave which will put a ripple on the top of the pulse wave form.
If you are making a wide band amplifier, there will be stray capacitance which will limit the bandwidth but adding inductors can increase the usable bandwidth but if not done correctly then overshoots will result.