Feb 8, 2017

My Bedtime Stories Now



Once upon a time, in 1802 to be exact,  the German scientist, E. F. F. Chladni (1756 1824) developed the method of placing sand on a vibrating plate to find its mode shapes and observed the beauty and intricacy of the modal patterns of the vibrating plates. 

In 1809 the French Academy invited Chladni to give a demonstration of his experiments. Napoléon Bonaparte, who attended the meeting, was so impressed he presented a sum of 3,000 francs to the academy, to be awarded to the first person to give a satisfactory mathematical theory of the vibration of plates. 

As the closing date of the competition in October 1811 approached, no brave candidate was showing up with attempts to conquer the physical reality with a mathematical model. Until only one candidate, Sophie Germain, entered the contest. But Lagrange, who was one of the judges, noticed an error in the derivation of her differential equation of motion so she was not granted the price. Regardless of her hard work, the model was incorrect and the examination was about results not efforts or process.

 The academy opened the competition again, with a new closing date of October 1813. Sophie Germain againwent through her model and entered the contest, presenting the correct form of the differential equation. However, the academy did not award the prize to her because the judges wanted physical justification of the assumptions made in her derivation. 

The competition was opened once more. In her third attempt, Sophie Germain was finally awarded the prize in 1815, although the judges were not completely satisfied with her theory. Sophie Germain took Napoléon's 3000 Francs and a valuable amount of knowledge and processing abilities.


And later, it was found that her differential equation was correct but the boundary conditions were erroneous. The correct boundary conditions for the vibration of plates were given in 1850 by G. R. Kirchhoff (1824 1887).

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