  We measure the spectral densities of fluctuations of an underdamped nonlinear
micromechanical oscillator. By applying a sufficiently large periodic
excitation, two stable dynamical states are obtained within a particular range
of driving frequency. White noise is injected into the excitation, allowing the
system to overcome the activation barrier and switch between the two states.
While the oscillator predominately resides in one of the two states for most
excitation frequencies, a narrow range of frequencies exist where the
occupations of the two states are approximately equal. At these frequencies,
the oscillator undergoes a kinetic phase transition that resembles the phase
transition of thermal equilibrium systems. We observe a supernarrow peak in the
power spectral densities of fluctuations of the oscillator. This peak is
centered at the excitation frequency and arises as a result of noise-induced
transitions between the two dynamical states.
