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Analysis of Diamond Cantilever Vibration (view source)
Revision as of 23:55, 3 March 2013
, 23:55, 3 March 2013→Results
==Results==
==Results==
The calculated values for $k$ show a positive, highly linear pattern. This results in the series of harmonic frequencies growing at an exponential rate. This created difficulties during the experimental phase; rapidly increasing frequencies caused a proportional drop in power/amplitude and made harmonics above three undetectable with our equipment. Increasing the amplification caused by the optical lever system to the degree needed to "see" those modes resulted in too great an uncertainty to be useful.
[[File:Data_Record.pdf]]
[[File:Data_Record.pdf]]
[[File:FirstFour.jpg]]
[[File:FirstFour.jpg]]
[[File:NonFirstFour.jpg]]
[[File:NonFirstFour.jpg]
Each eigenmode has one more node than the previous, starting with no nodes at all on the fundamental frequency. These were clearly visible on the lower harmonics. Because the absolute value of amplitude depends on power, these model-predicted functions need to be scaled to the experimental data and considered in terms of relative amplitude. The eigenmodes for cantilevers of nonuniform shape are similar to the uniform ones in overall shape and number of nodes, but show idiosyncrasies of increasing severity in correspondence with sharp changes in width. For example, a square wafer like the one to be used in the GlueX experiment shows a shift in the location of its nodes towards the slimmer ends of the cantilever, while a more slender shape shows much less of a shift.
==Conclusions==
==Conclusions==
Work on this project, like the overall GlueX project, is still ongoing. Current endeavers include comparing the experimental data to the results predicted by the models, in order to quantify any discrepancy there and determine possible improvements. Other considerations include improving the optical lever system, which reported data with too high an uncertainty value to consistently measure more than three modes above the fundamental frequency. The high uncertainty was mostly caused by scatter in the laser; this could be improved with the use of a laser with a higher Q factor or by decreasing the frequency of imperfections on the surface of the cantilevers.
Work on this project, like the overall GlueX project, is still ongoing. Current endeavers include comparing the experimental data to the results predicted by the models, in order to quantify any discrepancy there and determine possible improvements. Other considerations include improving the optical lever system, which reported data with too high an uncertainty value to consistently measure more than three modes above the fundamental frequency. The high uncertainty was mostly caused by scatter in the laser; this could be improved with the use of a laser with a higher Q factor or by decreasing the frequency of imperfections on the surface of the cantilevers.