  Nano-electromechanical systems implement the opto-mechanical interaction
combining electromagnetic circuits and mechanical elements. We investigate an
inductively coupled nano-electromechanical system, where a superconducting
quantum interference device (SQUID) realizes the coupling. We show that the
resonance frequency of the mechanically compliant string embedded into the
SQUID loop can be controlled in two different ways: (i) the bias magnetic flux
applied perpendicular to the SQUID loop, (ii) the magnitude of the in-plane
bias magnetic field contributing to the nano-electromechanical coupling. These
findings are quantitatively explained by the inductive interaction contributing
to the effective spring constant of the mechanical resonator. In addition, we
observe a residual field dependent shift of the mechanical resonance frequency,
which we attribute to the finite flux pinning of vortices trapped in the
magnetic field biased nanostring.
