  If an oscillator is driven by a force that switches between two frequencies,
the dynamics it exhibits depends on the precise manner of switching. Here we
take a one-dimensional oscillator and consider scenarios in which switching
occurs: (i) between two driving forces which have different frequencies, or
(ii) as a single forcing whose frequency switches between two values. The
difference is subtle, but entirely changes the long term behaviour, and
concerns whether the switch can be expressed linearly or nonlinearly in terms
of a discontinuous quantity (such as a sign or Heaviside step function that
represents the switch between frequencies). In scenario (i) the oscillator has
a stable periodic orbit, and the system can be described as a Filippov system.
In scenario (ii) the oscillator exhibits hidden dynamics, which lies outside
the theory of Filippov's systems, and causes the system to be increasingly (as
time passes) dominated by sliding along the frequency-switching threshold, and
in particular if periodic orbits do exist, they too exhibit sliding. We show
that the behaviour persists, at least asymptotically, if the systems are
regularized (i.e. if the switch is modelled as a smooth transition in the
manner of (i) or (ii)).
