Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and heavy-damping is derived. Besides, we prove in the under-damping, the oscillation is isochronous and the diminishing amplitude satisfies a rule of "constant ratio". All are done on a non-ODE basis.