Flow-induced vibration is a canonical issue in various engineering fields, leading to fatigue or immediate damage to structures. This paper numerically investigates flow-induced vibrations of a cylinder interacting with the wake of another cylinder at a Reynolds number Re = 150. It sheds light on the effects of mass ratio m*, damping ratio, and mass-damping ratio m*ζ on vibration amplitude ratio A/D at different reduced velocities Ur and cylinder spacing ratios L/D = 1.5 and 3.0. A couple of interesting observations are made. The m* has a greater influence on A/D than ζ although both m* and ζ cause reductions in A/D. The m* effect on A/D is strong for m* = 2−16 but weak for m* > 16. As opposed to a single isolated cylinder case, the mass-damping m*ζ is not found to be a unique parameter for a cylinder oscillating in a wake. The vortices in the wake decay rapidly at small ζ. Alternate reattachment of the gap shear layers on the wake cylinder fuels the vibration of the wake cylinder for L/D = 1.5 while the impingement and switch of the gap vortices do the same for L/D = 3.0.