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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: where m is the mass of an object, ? 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 3kx, 2kx, = mg -2kx, + 3kx, kx, = m,g kx, + kx, = mg

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: where m is the mass of an object, ? 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 3kx, 2kx, = mg -2kx, + 3kx, kx, = m,g kx, + kx, = mg

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
Problem 1.1MA
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use this matrix num sir

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k k m1 m2 k m2 X2 m3 m3 The system before release The system after release Figure Q3 ll all
Transcribed Image Text:k k m1 m2 k m2 X2 m3 m3 The system before release The system after release Figure Q3 ll all
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: Q3 d²x where m is the mass of an object, is the acceleration of an object, F, is downward force and F, is upward force. Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as (a) 2kx, 3kx, -2kx, + 3kr, mg kx, kx, + kr, m2g m;g %3D (b) Write the system of linear equations in Q3(a) in complete matrix form. (c) Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s² , g =9.8 1m/s² , m, is the first two digits of your matrix number, m, is m2 the last two digits of your matrix number and m, = + 5.5. 2 For example, a student with matrix number CD190028 will have m, = 19, m, = 28 and m, = 19.5
Transcribed Image Text: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: Q3 d²x where m is the mass of an object, is the acceleration of an object, F, is downward force and F, is upward force. Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as (a) 2kx, 3kx, -2kx, + 3kr, mg kx, kx, + kr, m2g m;g %3D (b) Write the system of linear equations in Q3(a) in complete matrix form. (c) Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s² , g =9.8 1m/s² , m, is the first two digits of your matrix number, m, is m2 the last two digits of your matrix number and m, = + 5.5. 2 For example, a student with matrix number CD190028 will have m, = 19, m, = 28 and m, = 19.5
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