This paper investigates the effect of repeated time-limited input signals on the output excursion of stable, linear time-invariant systems. It is first shown that the maximum norm of the output signal remains bounded if the repeated input signals are separated by a nonzero dwell time. Then a novel method for computing a tight bound on the output signal norm is proposed. The setting of the paper is motivated by a vehicle platooning application, where vehicles repeatedly open/close gaps in order to perform lane changes. The developed method analyzes driving safety by computing a bound on the spacing error between vehicles when performing repeated open/close gap maneuvers.