Analysis of Diamond Cantilever Vibration

Purpose
In order to facilitate coherent bremsstrahlung radiation, the movement of the diamond radiator due to natural oscillation must be minimized. One possible way to mount the diamond involves supporting it from a single corner and leaving the other end free. The purpose of this work is to theoretically model the free vibrations of such a system to determine if it is a realistic solution to the problem of mounting the diamond.

Method
The diamond, when mounted from one corner, can be approximately modeled as a cantilever (a beam fixed at one end and free at the other) with non-uniform width. In order to determine the natural oscillatory motion of the diamond, I decided to develop a mathematical model for the motion of cantilevers with non-uniform width, and test that model with data from physical cantilevers.