From hydrodynamics we know that the friction constant \xi is given by
\xi =6\pi \eta a/mwhere \eta is the viscosity of the solvent and a is the radius of the particle .
Solving the second equation in the previous slide we get
\mathbf{v}(t)=\mathbf{v}_{0}e^{-\xi t}+\int_{0}^{t}d\tau e^{-\xi (t-\tau )}\mathbf{F }(\tau ).