  Recent progress in observing and manipulating mechanical oscillators at
quantum regime provides new opportunities of studying fundamental physics, for
example, to search for low energy signatures of quantum gravity. For example,
it was recently proposed that such devices can be used to test quantum gravity
effects, by detecting the change in the [x,p] commutation relation that could
result from quantum gravity corrections. We show that such a correction results
in a dependence of a resonant frequency of a mechanical oscillator on its
amplitude, which is known as amplitude-frequency effect. By implementing this
new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q
sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave
resonator. Our experiments with sapphire resonator have established the upper
limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which
is a factor of 6 better than previously detected. The reasonable estimates of
$\beta_0$ from experiments with quartz resonators yield an even more stringent
limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum
period by Atkinson results in significantly stronger limitations on $\beta_0
\ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement
in these experiments, the exact upper bound on $\beta_0$ can not be reliably
established. Moreover, pendulum based systems only allow testing a specific
form of the modified commutator that depends on the mean value of momentum. The
electro-mechanical oscillators to the contrary enable testing of any form of
generalized uncertainty principle directly due to much higher stability and a
higher degree of control.
