b. In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition: 2k, - k2 = -4 4k, + 2k2 – kz = 9 -4k2 + 2k3 = -4 where k1, kz and kz are the spring constants of the three springs in newtons per metre (N/m). i. Solve the system of equations and find the values of k1, k2 and kg using the Inverse Matrix Method. Clearly show all steps when calculating the matrix inverse, including the calculation of the determinant and the adjoint. ii. Verify your answers by solving the same set of equations using Gaussian elimination. iii. Validate your answers to a and b above using appropriate mathematical software. Provide a screenshot of your code as part of the answer.

b. In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition: 2k, - k2 = -4 4k, + 2k2 – kz = 9 -4k2 + 2k3 = -4 where k1, kz and kz are the spring constants of the three springs in newtons per metre (N/m). i. Solve the system of equations and find the values of k1, k2 and kg using the Inverse Matrix Method. Clearly show all steps when calculating the matrix inverse, including the calculation of the determinant and the adjoint. ii. Verify your answers by solving the same set of equations using Gaussian elimination. iii. Validate your answers to a and b above using appropriate mathematical software. Provide a screenshot of your code as part of the answer.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition:

b. In order to ensure the stability of the crane, you decide to analyze the vibrations the crane
would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a
mass-spring system comprising three springs. The following equations are derived in the first
test condition:
2k, - k2 = -4
4k, + 2k2 – kz = 9
-4k2 + 2k3 = -4
where k1, kz and kz are the spring constants of the three springs in newtons per metre (N/m).
i.
Solve the system of equations and find the values of k1, k2 and kg using the Inverse Matrix
Method. Clearly show all steps when calculating the matrix inverse, including the
calculation of the determinant and the adjoint.
ii.
Verify your answers by solving the same set of equations using Gaussian elimination.
iii.
Validate your answers to a and b above using appropriate mathematical software. Provide
a screenshot of your code as part of the answer.

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