Sufficient conditions are given guaranteeing that every solution of the equation

\[x{\textquoteright}{\textquoteright}+h(t)x{\textquoteright}+\omega^2x=0 \qquad (h(t)\ge 0,\ x\in {\mathbb{R}})\]

and its derivative tend to zero as $t\to\infty$. The results are applicable in the general case $0\le 0\le h(t)\<\infty$, i.e., conditions $h(t)\ge$const.$\>0$ and $h(t)\le$const.$\<\infty$ are not required in general. In the first main theorem the damping is controlled on the whole half-line $[0,\infty)$. The second main theorem is devoted to the problem of the intermittent damping, when \ conditions are supposed only on the union of non-overlapping intervals.

}, keywords = {34D20, 70J25}, issn = {1056-2176}, doi = {10.12732/dsa.v27i2.6}, url = {https://acadsol.eu/dsa/articles/27/2/6.pdf}, author = {L. HATVANI} }