Resonance Frequency and Centre of Gravity Is there a relationship between these 2 
As of now I am moving a piece blutac up and down a ruler to change my COG. I have connected the base of my ruler to a vibration generator and am measuring the highest amplitude to measure the resonance frequency. 
The closer the COG is to to the base the higher my resonance frequency is.

 A: If you are talking about a pendulum in a gravitational field, yes there is a relationship between the two. If you do a free-body diagram and analyze the situation, you will get a differential equation:
$$\frac{\mathrm{d^2}\theta}{\mathrm{dt^2}}=\frac{-mgr}{\mathcal{I}}\sin\theta,$$
where 


*

*List item $\theta$ is the angular position relative to vertical (direction of the gravitational field of magnitude $g$,

*$t$ is time,

*$m$ is the mass of the pendulum,

*$r$ is the distance of the center of mass from the pivot point, and

*$\mathcal{I}$ is the moment of inertial about the pivot point in the plane of oscillation.


Based on this equation the angular frequency of (small) oscillations will be $$\Omega = \sqrt{\frac{mgr}{\mathcal{I}}},$$ which will be in radians per second if all the other quantities are in SI units.
So, a change in the position of CoM due to a moveable mass could change the frequency as long as the moment of inertia changes at a different rate. For a moveable mass on a stick, that is the case.
