  We begin by considering second order dynamical systems of the from $\ddot
x(t) + \gamma(t)\dot x(t) + \lambda(t)B(x(t))=0$, where $B: {\cal
H}\rightarrow{\cal H}$ is a cocoercive operator defined on a real Hilbert space
${\cal H}$, $\lambda:[0,+\infty)\rightarrow [0,+\infty)$ is a relaxation
function and $\gamma:[0,+\infty)\rightarrow [0,+\infty)$ a damping function,
both depending on time. For the generated trajectories, we show existence and
uniqueness of the generated trajectories as well as their weak asymptotic
convergence to a zero of the operator $B$. The framework allows to address from
similar perspectives second order dynamical systems associated with the problem
of finding zeros of the sum of a maximally monotone operator and a cocoercive
one. This captures as particular case the minimization of the sum of a
nonsmooth convex function with a smooth convex one. Furthermore, we prove that
when $B$ is the gradient of a smooth convex function the value of the latter
converges along the ergodic trajectory to its minimal value with a rate of
${\cal O}(1/t)$.
