Problem: Damped Oscillation

In a linear chain of lattice spacing a, particles of mass m are connected by first-neighbor springs of spring constant . In addition to the elastic forces, each particle is subjected to a damping force , where is the displacement of the nth particle from the equilibrium position, and is its velocity. How does the damping change the frequencies , and what is the relaxation time of the modes? Assume and discuss the and modes separately.