Two particle of respective masses mi = 4m and m2 = 3m are attached to two spring of %3D respective spring constants k and 3k as shown in the adjacent figure. k ; 4m 3k 3m a) Write down the Lagrangian of the system. b) Obtain Lagrange equations for each coordinate. c) Calculate the normal frequencies of the coupled oscillations. Deduce which frequency correspond to the symmetric and non-symmetric modes. d) Find the normal modes (eigenvectors) associated with the normal frequencies. e) Deduce a general solution for x1(t) and x2(1). f) Obtain a normal coordinate for each of the normal frequencies.

Two particle of respective masses mi = 4m and m2 = 3m are attached to two spring of %3D respective spring constants k and 3k as shown in the adjacent figure. k ; 4m 3k 3m a) Write down the Lagrangian of the system. b) Obtain Lagrange equations for each coordinate. c) Calculate the normal frequencies of the coupled oscillations. Deduce which frequency correspond to the symmetric and non-symmetric modes. d) Find the normal modes (eigenvectors) associated with the normal frequencies. e) Deduce a general solution for x1(t) and x2(1). f) Obtain a normal coordinate for each of the normal frequencies.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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