  Using a one-dimensional jellium model and standard beam theory we calculate
the spring constant of a vibrating nanowire cantilever. By using the asymptotic
energy eigenvalues of the standing electron waves over the nanometer-sized
cross-section area, the change in the grand canonical potential is calculated
and hence the force and the spring constant. As the wire is bent more electron
states fits in its cross section. This has an impact on the spring"constant"
which oscillates slightly with the bending of the wire. In this way we obtain
an amplitude-dependent resonance frequency of the oscillations that should be
detectable.
