


Over Damped Systems For overdamped systems, ζ > 1, so is real. This means that both p_{1} and p_{2} are both negative. The general solution for this case is for α = ωζ and β = , similar to the underdamped case. Note the lack of a complex term in the exponentials, so the system doesn't oscillate. Placing the initial conditions of x(0)=1 and x'(0)=0, the solution will be
A plot of this function with ζ = 3 and ω = 2π shows that the system decays slowly: 