  In this letter we discuss how to add forces to the Langevin equation. We
derive the exact generalized Langevin equation for the dynamics of one particle
subject to an external force embedded in a system of many interacting
particles. The external force may depend on time and/or on the phase-space
coordinates of the system. We construct a projection operator such that the
drift coefficient, the memory kernel, and the fluctuating force of the
generalized Langevin equation are the same as for the system without external
driving. We show that the external force then enters the generalized Langevin
equation additively. In addition we obtain one term which, to our knowledge,
has up to now been overlooked. We analyze this additional term for an exemplary
system.
