  When studying the motion of optically trapped particles on the $\mu s$ time
scale, in low viscous media such as air, inertia cannot be neglected.
Resolution of unusual and interesting behaviour not seen in colloidal trapping
experiments is possible. In attempt to explain the phenomena we use power
spectral methods to perform a parameter study of the Brownian motion of
optically trapped liquid aerosol droplets concentrated around the critically
damped regime. We present evidence that the system is suitably described by a
simple harmonic oscillator model which must include a description of
Fax\'{e}n's correction, but not necessarily frequency dependent hydrodynamic
corrections to Stokes' law. We also provide results describing how the system
behaves under several variables and discuss the difficulty in decoupling the
parameters responsible for the observed behaviour. We show that due to the
relatively low dynamic viscosity and high trap stiffness it is easy to transfer
between over- and under-damped motion by experimentally altering either trap
stiffness or damping. Our results suggest stable aerosol trapping may be
achieved in under-damped conditions, but the onset of deleterious optical
forces at high trapping powers prevents the probing of the upper stability
limits due to Brownian motion.
