  We revisit the problem of a triad of resonantly interacting nonlinear waves
driven by an external force applied to the unstable mode of the triad. The
equations are Hamiltonian, and can be reduced to a dynamical system for 5 real
variables with 2 conservation laws. If the Hamiltonian, $H$, is zero we reduce
this dynamical system to the motion of a particle in a one-dimensional
time-independent potential and prove that the system is integrable. Explicit
solutions are obtained for some particular initial conditions. When explicit
solution is not possible we present a novel numerical/analytical method for
approximating the dynamics. Furthermore we show analytically that when H=0 the
motion is generically bounded. That is to say the waves in the forced triad are
bounded in amplitude for all times for any initial condition with the single
exception of one special choice of initial condition for which the forcing is
in phase with the nonlinear oscillation of the triad. This means that the
energy in the forced triad generically remains finite for all time despite the
fact that there is no dissipation in the system. We provide a detailed
characterisation of the dependence of the period and maximum energy of the
system on the conserved quantities and forcing intensity. When $H \neq 0$ we
reduce the problem to the motion of a particle in a one-dimensional
time-periodic potential. Poincar\'{e} sections of this system provide strong
evidence that the motion remains bounded when $H \neq 0$ and is typically
quasi-periodic although periodic orbits can certainly be found. Throughout our
analyses, the phases of the modes in the triad play a crucial role in
understanding the dynamics.
