  Several branches of computing use a system's physical dynamics to do
computation. We show that the dynamics of an underdamped harmonic oscillator
can perform multifunctional computation, solving distinct problems at distinct
times within a dynamical trajectory. Oscillator computing usually focuses on
the oscillator's phase as the information-carrying component. Here we focus on
the time-resolved amplitude of an oscillator whose inputs influence its
frequency, which has a natural parallel as the activity of a time-dependent
neural unit. We call this unit an oscillatron. The activity of an oscillatron
at fixed time is a nonmonotonic function of the input, and so it can solve
nonlinearly-separable problems such as XOR. The activity of the oscillatron at
fixed input is a nonmonotonic function of time, and so it is multifunctional in
a temporal sense, able to carry out distinct nonlinear computations at distinct
times within the same dynamical trajectory. Time-resolved computing of this
nature can be done in or out of equilibrium, with the natural time evolution of
the system giving us multiple computations for the price of one.
