  A time dependent angular analysis of the decay mode $B_s \rightarrow J/\psi
\phi$ allows for the measurement of the mixing induced CP-violating phase
$\phi_s$. Within the Standard Model $\phi_s$ is theoretically precisely
predicted to be very small, however many Standard Model extensions predict
sizeable contributions to this phase. The current experimental knowledge of
$\phi_s$ has very larger uncertainties. However already with the data expected
to be delivered within the next year, the LHCb experiment at the Large Hadron
Collider at CERN, has the potential to improve significantly existing
measurements. In a data set of up to 37.5 pb$^{-1}$ taken in 2010, first
physics signals in the LHCb detector are reconstructed and their properties are
compared to Monte Carlo predictions. Based on recently published measurements
of $b\bar{b}$ cross-sections from the LHCb collaboration, the sensitivity on
the $CP$ violating phase $\phi_s$ in the decay $B_s \rightarrow J/\psi \phi$ is
evaluated. Additionally an alternative method to potentially extract
complementary information on $\phi_s$ from the measurement of the asymmetry in
semileptonic final states is presented.
