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, howev
er 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 $bbar{b}$ 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.
