  In this short note, we recover by a different method the new result due to
Attouch, Peyrouqet and Redont concerning the weak convergence as
$t\rightarrow+\infty$ of solutions $x(t)$ to the second order differential
equation \[ x^{\prime\prime}(t)+\frac{K}{t}x^{\prime}(t)+\nabla\Phi(x(t))=0, \]
where $K>3$ and $\Phi$ is a smooth convex function defined on an Hilbert Space
$\mathcal{H}.$ Moreover, we improve slightly their result on the rate of
convergence of $\Phi(x(t))-\min\Phi.$
