


Critically Damped Systems A critically damped system has ζ = 1, so p_{1} = p_{2} = ζω. This means that one of the solutions is The other linearly independent solution can be found by using the reduction of order method. This gives the solution Using the initial conditions x(0) = 1 and x'(0) = 0 as in the under and overdamped cases, the solution is now
A plot of this solution for ω = 2π looks like Note that a critically damped system converges to zero faster than any other without oscillating. 