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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

See similar textbooks