You could compute the stiffness of each length of the beam using Bernoulli beam theory and show that putting the high stiffness section closest to the base reduces the tip deflection the most.
I have provided many images of a Kinematic Mount. Here is one using three balls in three Vees created by a pair of cylindrical pins with magnets at the center to pull the two plates together.
While the total mass and stiffness stays the same, the distribution of mass plays a large role in the modal frequencies.