Past exam of the physics A course of the University of Cambridge / 2015 / Paper 2 / Section B / B6 / b

For $b^2=4mk$, the repeated characteristic root requires a second linearly independent solution $t{e}^{-\gamma t}$:This is critical damping. If $x(0)=x_0$ and $\dot{x}(0)=0$, then $x=x_0(1+\gamma t)e^{-\gamma t}$, demonstrating the monotone return used in the suspension discussion.