Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a series of springs. To develop a mathematical model of the spring-mass system, Newton's second law can be employed in conjunction with force balances. For each mass, the Newton's second law can be expressed as: m=F, -F, where m is the mass of an object, is the acceleration of an object, F, is downward force and F, is upward force. (a) Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as = mg 2kx; -2kx, + 3kx, 3kx, kx, = m,g kx, + kx, = m,g (b) Write the system of linear equations in Q3(a) in complete matrix form. Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s² , g = 9.8 Im/s² , m, is the first two digits of your matrix number, m, is the last two digits of your matrix number and m, = (c) For example, a student with matrix number CD190028 will have m, =19, m, = 28 and m, = 19.5

Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a series of springs. To develop a mathematical model of the spring-mass system, Newton's second law can be employed in conjunction with force balances. For each mass, the Newton's second law can be expressed as: m=F, -F, where m is the mass of an object, is the acceleration of an object, F, is downward force and F, is upward force. (a) Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as = mg 2kx; -2kx, + 3kx, 3kx, kx, = m,g kx, + kx, = m,g (b) Write the system of linear equations in Q3(a) in complete matrix form. Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s² , g = 9.8 Im/s² , m, is the first two digits of your matrix number, m, is the last two digits of your matrix number and m, = (c) For example, a student with matrix number CD190028 will have m, =19, m, = 28 and m, = 19.5

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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