Using the Maxwell-Bloch equations, we have studied dynamics associated with an electro-optically tunable laser modulated by a sinusoidal signal with a frequency near the cavity free spectral range. We find that frequency modulation (FM) modelocking may occur when a higher order FM mode acquires the lowest threshold. For short-cavity lasers, the pulse waveform in modelocking is complicated, and unlike the simple Gaussian shape suggested by previous studies. In order to explain instability observed in laser FM operation, we develop a linear stability analysis for the lasing FM mode. Our analysis shows that this type of instability is attributed to mode competition and to laser relaxation dynamics. We then confirm the analytic results with numerical simulations.