We rewrite $$ mu'' + f(u') + s(u) = F(t),\quad u(0)=I,\ u'(0)=V,\ t\in (0,T] $$ as a first-order ODE system $$ \begin{align*} u' &= v \\ v' &= m^{-1}\left(F(t) - f(v) - s(u)\right) \end{align*} $$
