This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator
x
+
h
(
t
)
x
′
+
ω
2
x
=
0
\begin{equation*} x + h(t)\!\:x’ + \omega ^2x = 0 \end{equation*}
is uniformly asymptotically stable, where
h
:
[
0
,
∞
)
→
[
0
,
∞
)
h\!: [0,\infty ) \to [0,\infty )
is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient
h
h
. The obtained sufficient conditions are compared with known conditions for uniform asymptotic stability. Two diagrams are included to facilitate understanding of the conditions. By giving a concrete example, remaining problems are pointed out.