  We study a Langevin equation describing the Brownian motion of an object
subjected to a viscous drag, an external constant force, and a solid friction
force of the Coulomb type. In a previous work [H. Touchette, E. Van der
Straeten, W. Just, J. Phys. A: Math. Theor. 43, 445002, 2010], we have
presented the exact solution of the velocity propagator of this equation based
on a spectral decomposition of the corresponding Fokker-Planck equation. Here,
we present an alternative, exact solution based on the Laplace transform of
this equation, which has the advantage of being expressed in closed form. From
this solution, we also obtain closed-form expressions for the Laplace transform
of the velocity autocorrelation function and for the power spectrum, i.e., the
Fourier transform of the autocorrelation function. The behavior of the power
spectrum as a function of the dry friction force and external forcing shows a
clear crossover between stick and slip regimes known to occur in the presence
of solid friction.
