  We show that in periodically driven systems, along with the delta-peak at the
driving frequency, the spectral density of fluctuations displays extra
features. These can be peaks or dips with height quadratic in the driving
amplitude, for weak driving. For systems where inertial effects can be
disregarded, the peaks/dips are generally located at zero frequency and at the
driving frequency. The shape and intensity of the spectra very sensitively
depend on the parameters of the system dynamics. To illustrate this sensitivity
and the generality of the effect, we study three types of systems: an
overdamped Brownian particle (e.g., an optically trapped particle), a two-state
system that switches between the states at random, and a noisy threshold
detector. The analytical results are in excellent agreement with numerical
simulations.
