A detailed investigation is made into the effect of inherent transportation lag on the nature of limit cycles sustained in a second-order sampled-data system containing a relay type non-linearity. The effectiveness of the either signals of sinusoidal, triangular and square wave shape to suppress limit cycles is studied in detail and the advantages and disadvantages of each wave shape are discussed. The method of analysis is via the state transition technique and it is advantageously used to evaluate the response of the system until a final steady-state value is attained by the controlled variable.