We perform a large number of simulations over a wide range of system parameters to approximate the basins of attraction of steady oscillating solutions. We find that the basins of attraction vary as a function of system parameters and initial conditions. For large equilibrium separations, the basin of attraction is dominated by the low-amplitude solution. The location of the fixed point is shifted toward the higher values of instantaneous displacement and velocity for larger equilibrium separations. We show that the basin of attraction in the neighborhood of the fixed point is dominated by low-amplitude solutions as relative humidity is increased.