  A one dimensional trap model for a thermally activated classical particle is
introduced to simulate driven dynamics in presence of "ageing" effects. The
depth of each trap increases with the time elapsed since the particle has
fallen into it. The consequences of this dynamical pinning are studied, and
velocity-force characteristics are numerically obtained. A special attention is
paid to the situation where the particle is pulled with a spring to ensure a
finite average velocity. In the low velocity regime, the presence of a broad
distribution of trapping times leads to suppression of linear response,
replaced by a threshold or by sublinear dynamics. A regime of strong
fluctuations is obtained when the particle is driven at intermediate
velocities.
