1. The problem statement, all variables and given/known data Let ay'' + by' +cy = R(x) Determining whether a system is under/over/critically damped depends on the size of b^2 compared to 4ac. Does it depend at all on R(x)? 2. Relevant equations Characteristic equation, quadratic equation. 3. The attempt at a solution I've found a general solution to a D.E. where b^2 < 4ac, and is therefore underdamped (if the D.E = 0) However, I'm not sure if I can still conclude that the system is underdamped if the D.E. = R(x).