The friction force at joints of engineering structures is usually unknown and not directly identifiable. This contribution explores a procedure for obtaining the governing equation of motion and correctly identifying the unknown Coulomb friction force of a mass-springdashpot system. In particular, a single degree-of-freedom system is investigated both numerically and experimentally. The proposed procedure extends the state-of-the-art datadriven sparse identification of nonlinear dynamics (SINDy) algorithm by developing a methodology that explicitly imposes constraints encoding knowledge of the nonsmooth dynamics experienced during stick-slip phenomena. The proposed algorithm consists of three steps: (i) data segregation of mass-motion from mass-sticking during stick-slip response; (ii) application of SINDy on the mass-motion dataset to obtain the functional form of the governing equation; and (iii) applying sticking and slipping conditions to identify the unknown system parameters. It is shown that the proposed approach yields an improved estimate of the uncertain system parameters such as stiffness, viscous damping, and magnitude of friction force (all mass normalized) for various signal-to-noise ratios compared to SINDy.