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A discrete-time-domain numerical method for simulating complete sinusoidal oscillator properties is discussed. Two modes for the spontaneous starting of oscillations can be simulated. The first mechanism results from the remnant electrical noise in the circuit, and the second mechanism is due to the transients when the power supply is switched on abruptly. The amplifier nonlinearities, as well as the automatic amplitude control function, can also be incorporated into the simulation. Very efficient computational algorithms for the major classes of real oscillators are presented. Experimental results show the accuracy of the simulated results. It is suggested that this simulation method can be used as a powerful tool for both transient and steady-state analysis, and for the design of sinusoidal oscillators.