  Coupled electromechanical resonators that can be independently
driven/detected and easily integrated with external circuits are essential for
exploring mechanical modes based signal processing. Here, we present a room
temperature phonon-cavity electromechanical system, consisting of two distinct
resonators: a silicon nitride electromechanical drum capacitively coupled to an
aluminum one. We demonstrate electromechanically induced transparency and
amplification in a two-tone driving scheme and observe the phonon-cavity force
affecting the mechanical damping rates of both movable objects. We also develop
an analytical model based on linearly coupled motion equations, which captures
the optomechanical features in the classical limit and enables to fit
quantitatively our measurements. Our results open up new possibilities in the
study of phonon-cavity based signal processing in the classical and potentially
in the future in the quantum regimes.
