In this paper, we consider the problem of vehicle following control with delay. To solve the problem of traffic congestion, one of the solutions to be considered consists in organizing the traffic into platoons, that is groups of vehicles including a leader and a number of followers "tightly" spaced, all moving in a longitudinal direction. Excepting the stability of individual cars, the problem of avoidance of slinky type effects will be explicitly discussed. Sufficient conditions on the set of control parameters to avoid such a phenomenon will be explicitly derived in a frequency-domain setting.