In this talk, we clarify the relationship between some sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator

is uniformly asymptotically stable, where h is locally integrable. Four conditions are compared. All conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. We compare the obtained sufficient conditions with known conditions for uniform asymptotic stability. We show a relationship diagram to facilitate understanding between conditions. We also point out the remaining problems by giving a concrete example.