  This book chapter describes the dynamics of a modulated oscillator for
resonant and nonresonant modulation. Two types of resonant modulation are
considered: additive, with frequency close to the oscillator eigenfrequency,
and parametric, with frequency close to twice the eigenfrequency. It is shown
that relaxation of the oscillator is accompanied by quantum noise, which leads
to a finite-width distribution over quantum states even for T=0. The quantum
noise also leads to switching between coexisting vibrational states via
transitions over the barrier in phase space. The switching mechanism, quantum
activation, has no analog in thermal equilibrium systems. The switching rates
display characteristic scaling near bifurcation points. The power and
absorption/amplification spectra of modulated oscillators are studied,
including their fine structure. Nonresonant modulation can lead to cooling,
heating, or self-sustained vibrations of an oscillator. The relation between
the previously discussed direct nonresonant excitation of the oscillator and
the excitation mechanism studied in optomechanics is analyzed.
