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Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T and mass per unit length μ is pinned at x = 0 and x = L. The string is free to vibrate, and its first vibration mode is shown below. Vo V2 first mode In order to find the frequency of the first mode (or fundamental frequency), the string is discretized into a certain number of linear elements. The stiffness and mass matrices of the i-th element are, respectively T 1 - ESMi = Li - Lift 2 1 EMM₁ = 6 1 [1] 2 (2) (a) [5pts] What is the minimum number of linear elements necessary to compute the fun- damental frequency of the vibrating string? (b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency of vibration of the string.

Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T and mass per unit length μ is pinned at x = 0 and x = L. The string is free to vibrate, and its first vibration mode is shown below. Vo V2 first mode In order to find the frequency of the first mode (or fundamental frequency), the string is discretized into a certain number of linear elements. The stiffness and mass matrices of the i-th element are, respectively T 1 - ESMi = Li - Lift 2 1 EMM₁ = 6 1 [1] 2 (2) (a) [5pts] What is the minimum number of linear elements necessary to compute the fun- damental frequency of the vibrating string? (b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency of vibration of the string.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T and
mass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and its
first vibration mode is shown below.
In order to find the frequency of the first mode (or fundamental frequency), the string is
discretized into a certain number of linear elements. The stiffness and mass matrices of the
i-th element are, respectively
ESMi =
T
Li

1 −1
−1 1 
EMMi =
Liµ
6

2 1
1 2 
. (2)
(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?
(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency of
vibration of the string

Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T and mass per unit length μ is pinned at x = 0 and x = L. The string is free to vibrate, and its first vibration mode is shown below. Vo V2 first mode In order to find the frequency of the first mode (or fundamental frequency), the string is discretized into a certain number of linear elements. The stiffness and mass matrices of the i-th element are, respectively T 1 - ESMi = Li - Lift 2 1 EMM₁ = 6 1 [1] 2 (2) (a) [5pts] What is the minimum number of linear elements necessary to compute the fun- damental frequency of the vibrating string? (b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency of vibration of the string.
Transcribed Image Text:Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T and mass per unit length μ is pinned at x = 0 and x = L. The string is free to vibrate, and its first vibration mode is shown below. Vo V2 first mode In order to find the frequency of the first mode (or fundamental frequency), the string is discretized into a certain number of linear elements. The stiffness and mass matrices of the i-th element are, respectively T 1 - ESMi = Li - Lift 2 1 EMM₁ = 6 1 [1] 2 (2) (a) [5pts] What is the minimum number of linear elements necessary to compute the fun- damental frequency of the vibrating string? (b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency of vibration of the string.
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