  We use active microrheology to determine the frequency dependent moduli of a
linear viscoelastic fluid in terms of the polymer time constant ($\lambda$),
and the polymer ($\mu_p$) and solvent viscosity ($\mu_s$), respectively. We
measure these parameters from the response function of an optically trapped
Brownian probe in the fluid under an external perturbation, and at different
dilutions of the viscoelastic component in the fluid. This is an improvement
over bulk microrheology measurements in viscoelastic Stokes-Oldroyd B fluids
which determine the complex elastic modulus $G(\omega)$ of the fluid, but do
not, however, reveal the characteristics of the polymer chains and the
Newtonian solvent of the complex fluid individually. In a recent work [Paul
\textit{et al}., 2018 J. Phys. Condens. Matter \textbf{30} 345101], we
linearized the Stokes-Oldroyd B fluid model and thereby explicitly formulated
the frequency dependent moduli in terms of ($\mu_p$) and ($\mu_s$), which we
now extend to account for an external sinusoidal force applied to the probe
particle. We measure $\lambda$, $\mu_p$, and $\mu_s$ experimentally, and
compare with existing the $\lambda$ values in the literature for the same fluid
at some of the dilution levels, and obtain good agreement. Further, we use
these parameters to calculate the complex elastic modulus of the fluid again at
certain dilutions and verify successfully with existing data. This establishes
our method as an alternate approach in the active microrheology of complex
fluids which should reveal information about the composition of such fluids in
significantly greater detail and high signal to noise.
