InterviewSolution
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InterviewSolution
| 1. |
Can you give the proof of formula wl3/4bd3Y |
| Answer» I was not able to write it in a proper way man sorry<br>If you want, you can use the calculus of variations to find a steady-state y minimizing potential energy. It is not too hard: take the correct expression U=∫dx(F(x)y(x)−YI[y′′(x)]2)U=∫dx(F(x)y(x)−YI[y″(x)]2) and replace y(x)→y(x)+δy(x)y(x)→y(x)+δy(x), looking for δU=∫dx(F δy−Y I [(y′′+δy′′)2−(y′′)2])=0δU=∫dx(F δy−Y I [(y″+δy″)2−(y″)2])=0. Ignoring (δy′′)2(δy″)2 you integrate by parts twice: ∫dx(F−Y I y′′′′)δy=0∫dx(F−Y I y⁗)δy=0 can only be 00 for all δyδy if F=Y I y′′′′.F=Y I y⁗. (But, F(x) does have a δ function | |